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\title{Rethinking Hyperparameter Optimization for Efficient and Explainable Machine Learning in Civic Health Decision-Making: Empirical Evidence from Malaria Diagnosis}

\author{
Olushina Olawale Awe\textsuperscript{1*}, Julia Soares de Souza\textsuperscript{2},
Anderson Kaue Bittencourt Cruz\textsuperscript{2}, 
Olukorede Olabanji Adekunle\textsuperscript{3*}, 
Paul J. Owolabi\textsuperscript{4}, and
Emmanuel Olusola Oladeji\textsuperscript{5} \\
\\
\textsuperscript{1} Statistical Learning Laboratory, Federal University of Bahia, Brazil \\
\textsuperscript{2} Department of Statistics, State University of Campinas, Brazil \\
\textsuperscript{3} Department of Surgery, University of Ilorin Teaching Hospital, Ilorin, Nigeria \\
\textsuperscript{4} Covenant Applied Informatics and Communications Africa Center of Excellence (CApiC-ACE),\\ Covenant University, Ota, Nigeria \\
\textsuperscript{5} Surgery Interest Group of Africa, Lagos, Nigeria \\
\\
\textsuperscript{*}Corresponding author emails: olukorede.adekunle@npmcn.edu.ng, oawe@unicamp.br
}

\date{}

\begin{document}

\maketitle



\begin{bmcabstract}
%Malaria remains one of the most persistent infectious diseases worldwide, causing hundreds of millions of infections annually and placing a significant burden on healthcare systems, particularly in low-resource regions. Machine learning has emerged as a promising tool for improving malaria diagnosis and supporting clinical decision-making; however, the practical deployment of such models is often constrained by the complexity and computational cost associated with hyperparameter optimization. This study presents a comprehensive empirical comparison of stochastic and deterministic hyperparameter optimization strategies for supervised machine learning models applied to malaria diagnosis. Five optimization strategies—Grid Search, Random Search, Bayesian Optimization, Genetic Algorithms, and Hyperband Racing—were evaluated across six supervised learning algorithms: Random Forest, Neural Networks, Support Vector Machines, Logistic Regression, XGBoost, and K-Nearest Neighbors. The models were trained using both synthetic datasets with varying levels of complexity and a real clinical malaria dataset consisting of 250 patients with 16 clinical features. Model performance was assessed using repeated 10-fold cross-validation with five repetitions, and evaluation metrics included F1-score, accuracy, ROC AUC, Matthews Correlation Coefficient, and balanced accuracy. Class imbalance was addressed through SMOTE oversampling, while model interpretability was investigated using LIME, SHAP, and Permutation Feature Importance techniques. The results indicate that stochastic and deterministic optimization strategies produced statistically comparable diagnostic performance, with mean F1-scores of 0.657 and 0.653 respectively (difference <1\%). Random Search demonstrated approximately three times greater computational efficiency than Bayesian Optimization. Variance decomposition analysis revealed that dataset characteristics and algorithm selection accounted for most of the performance variability (68.5\% and 16.3\% respectively), whereas the choice of hyperparameter optimization strategy contributed less than 5\%. After class balancing and hyperparameter tuning, Random Forest achieved the highest predictive performance (F1-score: 0.831; ROC AUC: 0.870). Explainability analyses consistently identified age, coca-cola urine, prostration, hyperpyrexia, and convulsions as the most influential predictive features across multiple interpretability methods. These findings suggest that relatively simple hyperparameter optimization strategies are sufficient for developing effective machine learning models for malaria diagnosis, achieving clinically meaningful performance while maintaining substantially lower computational requirements. The results support a pragmatic modeling framework that prioritizes data quality, algorithm selection, and computational efficiency over complex optimization procedures, particularly in resource-constrained healthcare environments where the malaria burden remains highest.

\textbf{Background:} Malaria remains one of the most persistent infectious diseases worldwide, with hundreds of millions of cases annually. Machine learning has emerged as a promising tool for malaria diagnosis, but the practical deployment of these models is constrained by hyperparameter optimization complexity. This study provides a comprehensive comparison of stochastic and deterministic hyperparameter optimization strategies for supervised machine learning models applied to malaria diagnosis.

\textbf{Methods:} We evaluated five optimization strategies (Grid Search, Random Search, Bayesian Optimization, Genetic Algorithms, and Hyperband Racing) across six supervised learning algorithms (Random Forest, Neural Networks, Support Vector Machines, Logistic Regression, XGBoost, and K-Nearest Neighbors). Models were trained on synthetic datasets with varying complexity and a real clinical malaria dataset comprising 250 patients with 16 clinical features. Performance was assessed using 10-fold cross-validation repeated five times, with evaluation metrics including F1-score, accuracy, ROC AUC, Matthews Correlation Coefficient, and balanced accuracy. Class imbalance was addressed using SMOTE oversampling, and model interpretability was examined through LIME, SHAP, and Permutation Feature Importance analyses.

\textbf{Results:} Stochastic and deterministic optimization strategies yielded statistically equivalent diagnostic performance, with mean F1-scores of 0.657 and 0.653 respectively (difference < 1\%). Random Search demonstrated nearly three times higher computational efficiency than Bayesian Optimization. Algorithm selection and dataset characteristics dominated performance variability, accounting for 16.3\% and 68.5\% of total variance respectively, while optimization strategy contributed less than 5\%. After class balancing and hyperparameter tuning, Random Forest achieved the highest performance (F1-score: 0.831, ROC AUC: 0.870). Explainability analyses consistently identified age, coca-cola urine, prostration, hyperpyrexia, and convulsions as key predictive features across multiple methods.

\textbf{Conclusions:} Simple hyperparameter optimization strategies are sufficient for effective clinical deployment of malaria diagnostic models, achieving clinically acceptable performance with minimal computational requirements. The findings support a pragmatic modeling approach prioritizing data quality, algorithm selection, and computational efficiency over optimization complexity, particularly relevant for resource-constrained healthcare settings where malaria burden is highest.
\end{bmcabstract}

\keywords{Malaria diagnosis, Machine learning, Hyperparameter optimization, SMOTE, Model explainability}

\section{Introduction}

Malaria remains one of the most persistent and consequential infectious diseases worldwide, representing a substantial burden for public health systems, particularly in low- and middle-income countries \cite{ref1, ref2}. Despite decades of civic global health control efforts, the disease continues to cause hundreds of millions of infections annually, with mortality concentrated among vulnerable populations such as children under five years of age and pregnant women. According to estimates from the World Health Organization, malaria accounted for approximately 247 million cases and more than 600,000 deaths globally in 2021, with sub-Saharan Africa bearing the overwhelming majority of this burden \cite{ref1, ref2, ref4}. These figures underscore the persistent challenges associated with malaria control and highlight the critical importance of effective diagnostic strategies in reducing morbidity and mortality.

Accurate and timely diagnosis plays a central role in malaria case management, surveillance, and epidemiological monitoring \cite{ref5}. Early detection enables prompt treatment, reduces the risk of severe disease progression, and limits onward transmission within communities. Traditionally, malaria diagnosis relies on light microscopy of stained blood smears and rapid diagnostic tests (RDTs) \cite{ref6}. Microscopy is widely regarded as the reference standard due to its ability to quantify parasitaemia and differentiate Plasmodium species; however, its effectiveness is highly dependent on trained personnel, laboratory infrastructure, and consistent access to electricity. These requirements pose substantial barriers in remote and resource-constrained settings, where malaria prevalence is often highest. Rapid diagnostic tests, while more accessible and easier to deploy, exhibit considerable variability in diagnostic performance, particularly in cases of low parasitaemia, mixed infections, or antigen persistence following treatment \cite{ref7, ref8, ref9, ref10}. Consequently, limitations in sensitivity, specificity, and operational reliability continue to motivate the exploration of alternative diagnostic approaches.

In recent years, machine learning has emerged as a powerful tool in health informatics, offering novel opportunities for disease detection, risk stratification, and clinical decision support \cite{ref11, ref12}. By using computational models that learn complex patterns from data, machine learning methods have demonstrated promising performance across a wide range of medical applications, including infectious disease diagnosis \cite{ref38}. In the context of malaria, prior studies have explored both image-based approaches, such as deep learning models applied to microscopic blood smear images \cite{ref13, ref14, ref15}, and data-driven approaches based on clinical, demographic, or laboratory variables \cite{ref16, ref17}. These methods have shown the potential to augment or partially automate diagnostic processes, particularly in settings where expert microscopists are scarce. Despite these advances, the practical deployment of machine learning models in real-world healthcare environments remains constrained by several methodological and operational challenges \cite{ref18, ref19}. Among these, the process of hyperparameter optimization represents a critical yet underexplored aspect of model development. Hyperparameters govern key properties of machine learning algorithms, such as model complexity, learning dynamics, and regularization strength, and their configuration can substantially influence predictive performance. While numerous optimization strategies have been proposed, ranging from simple exhaustive searches to sophisticated probabilistic and evolutionary methods \cite{ref20, ref21, ref22, ref23, ref24}, the relative benefits of these approaches in applied clinical contexts are not well understood.

  Healthcare systems in malaria-endemic regions often operate under severe resource constraints, including limited computational infrastructure, restricted access to high-performance hardware, and the need for rapid model retraining or adaptation. In such environments, optimization strategies that are computationally intensive or difficult to implement may be impractical, regardless of their theoretical appeal. Consequently, understanding whether complex hyperparameter optimization techniques offer meaningful advantages over simpler alternatives is of both scientific and practical importance \cite{ref25, ref26}. One of the central challenges in applied machine learning is hyperparameter optimization, which plays a critical role in determining model performance. A wide range of optimization strategies has been proposed, broadly categorized into deterministic approaches (e.g., Grid Search, Bayesian Optimization) and stochastic approaches (e.g., Random Search, Genetic Algorithms, Hyperband). Among these, Bayesian Optimization has received considerable attention due to its strong theoretical foundation in probabilistic surrogate modeling and efficient exploration of high-dimensional parameter spaces. Consequently, it is often implicitly regarded as a necessary component of high-quality model development in modern machine learning pipelines. However, this prevailing assumption raises an important question: Do increasingly sophisticated hyperparameter optimization strategies yield meaningful performance improvements in real-world healthcare applications, particularly under practical constraints such as limited computational resources, noisy data, and class imbalance?

This question is especially relevant in low- and middle-income settings, where computational infrastructure, technical expertise, and data quality may be limited. In such contexts, the adoption of computationally intensive optimization techniques may not be feasible, and the marginal performance gains—if any—must be carefully weighed against their operational cost. Moreover, recent advances in statistical learning theory suggest that model performance is often more strongly influenced by algorithm selection, data quality, and feature representation than by fine-grained optimization of hyperparameters. Against this backdrop, the present study aims to provide a comprehensive and methodologically grounded comparison of stochastic and deterministic hyperparameter optimization strategies for supervised machine learning models applied to malaria diagnosis. By evaluating multiple algorithms across synthetic datasets of varying complexity and a real clinical dataset, this work seeks to disentangle the relative contributions of data characteristics, algorithm choice, and optimization strategy to diagnostic performance. In doing so, the study addresses a critical gap in the literature and offers practical guidance for researchers and practitioners seeking to develop machine learning-based diagnostic tools that are both effective and deployable in resource-constrained healthcare environments.

\section{Related Works}

Existing literature tends to emphasize algorithmic performance, frequently reporting marginal gains achieved through increasingly sophisticated optimization procedures. However, these gains are rarely evaluated in relation to their computational cost, stability across datasets, or relevance to deployment scenarios typical of low-resource healthcare settings. Moreover, comparative analyses that systematically contrast stochastic and deterministic optimization strategies across multiple learning algorithms and datasets remain scarce, particularly in the domain of malaria diagnosis. The application of machine learning to malaria diagnosis has expanded considerably over the past decade, reflecting broader trends in the adoption of data-driven methods within biomedical research. Early studies primarily focused on image-based analysis of Giemsa-stained blood smears, leveraging classical computer vision techniques to identify parasitized red blood cells. With the advent of deep learning, convolutional neural networks have been widely employed to automate parasite detection and classification \cite{ref13, ref14, ref15}, often achieving performance comparable to or exceeding that of trained microscopists under controlled conditions. These approaches have demonstrated high sensitivity and specificity in curated datasets, highlighting the potential of machine learning to support or augment traditional diagnostic workflows.

Parallel to image-based methods, several studies have explored the use of structured clinical and laboratory data for malaria diagnosis \cite{ref17}. These approaches typically employ supervised learning algorithms, such as logistic regression, decision trees, random forests, support vector machines, and ensemble methods, to model the relationship between patient-level variables and infection status. Clinical features commonly include demographic characteristics, reported symptoms, vital signs, and basic laboratory measurements. Such models offer advantages in terms of interpretability and ease of integration into existing clinical information systems, particularly in settings where access to high-quality microscopy images may be limited. While predictive performance has been the primary focus of much of this literature, fewer studies have examined the methodological aspects of model development that influence reproducibility and deployment feasibility. In particular, hyperparameter optimization is often treated as a secondary concern, with limited reporting on search strategies, computational budgets, or sensitivity to parameter choices. Grid search remains a commonly used approach due to its conceptual simplicity and ease of implementation, despite its well-known inefficiency in high-dimensional search spaces. Random search has been proposed as a more efficient alternative \cite{ref20}, with theoretical and empirical evidence suggesting that it can outperform grid search when only a subset of hyperparameters substantially influences model performance.

More recently, advanced optimization techniques such as Bayesian optimization \cite{ ref22}, genetic algorithms \cite{ref23}, and bandit-based methods \cite{ref24} have gained traction within the machine learning community. Bayesian optimization, in particular, has been promoted as a principled approach that balances exploration and exploitation by constructing probabilistic surrogate models of the objective function. Evolutionary algorithms and racing methods aim to efficiently allocate computational resources by iteratively refining candidate configurations or discarding poorly performing options. Although these methods have demonstrated success in benchmark optimization tasks, their advantages in applied clinical settings are less clear.

Within the broader healthcare machine learning literature, several authors have raised concerns regarding the mismatch between methodological sophistication and practical utility \cite{ref18, ref19}. Studies comparing optimization strategies across different domains have reported diminishing returns associated with increasingly complex methods, especially when dataset size, noise, or class imbalance dominate performance variability. In medical applications, where datasets are often heterogeneous and limited in size, the stability and interpretability of models may be more critical than marginal improvements in predictive metrics. In the specific context of malaria diagnosis, systematic comparisons of hyperparameter optimization strategies remain limited. Existing studies typically evaluate a single optimization method or focus exclusively on maximizing accuracy without assessing computational efficiency or robustness across datasets \cite{ref25, ref26, ref27}. Moreover, few investigations explicitly consider the implications of optimization choices for deployment in low-resource environments, where constraints on time, hardware, and technical expertise are paramount.

The present study builds upon this body of work by conducting a structured and statistically grounded comparison of stochastic and deterministic hyperparameter optimization strategies across multiple supervised learning algorithms. By incorporating both synthetic datasets, designed to isolate the effects of feature interactions and class separability, and real clinical data, this work provides a balanced assessment of how optimization strategies interact with data characteristics and model choice. In contrast to prior studies that emphasize algorithmic novelty, the focus here is on methodological clarity, reproducibility, and practical relevance, aligning with principles commonly emphasized in applied biometry and medical statistics \cite{ref29}.

Recent studies have explored the interaction between model architecture and optimization strategies in malaria diagnosis. Comparisons between Transformer-based models and convolutional neural networks suggest that while advanced architectures can improve performance, gains from hyperparameter tuning are often marginal under computational constraints \cite{ref31}.

Transfer learning approaches integrating clinical and image-based features have further emphasized the importance of efficiency and robustness over architectural complexity \cite{ref32}. In parallel, growing attention has been given to explainability, with methods such as SHAP and LIME enabling more transparent decision-making in clinical contexts \cite{ref33,ref34}.

Additionally, recent works demonstrate that dataset characteristics and preprocessing choices often dominate performance improvements, outweighing the effects of optimization strategies \cite{ref35}. These findings motivate the present study. Despite the growing body of literature on machine learning in healthcare, there remains a notable gap in systematically quantifying the relative contribution of hyperparameter optimization strategies compared to other key determinants of model performance. Most existing studies either focus on a single optimization method or evaluate performance within narrowly defined experimental settings, limiting their generalizability. Furthermore, few studies explicitly examine the trade-off between predictive performance and computational efficiency, which is of paramount importance in clinical deployment.

To address this gap, the present study provides a comprehensive empirical evaluation of stochastic and deterministic hyperparameter optimization strategies in the context of machine learning–based malaria diagnosis. Specifically, we compare five widely used optimization methods like Grid Search, Random Search, Bayesian Optimization, Genetic Algorithms, and Hyperband Racing, across six supervised learning algorithms and multiple datasets with varying levels of complexity. In addition to standard performance metrics such as accuracy, F1-score, and ROC AUC, we introduce computational efficiency as a key evaluation criterion, reflecting the practical constraints of real-world healthcare environments.

\section{Methods}

\subsection{Study design and analytical framework}

This study adopts a comparative methodological design aimed at evaluating the impact of hyperparameter optimization strategies on the diagnostic performance of supervised machine learning models for malaria classification. The analytical framework was structured to isolate, as much as possible, the contributions of three key components: data characteristics, learning algorithm, and hyperparameter optimization strategy. To this end, multiple datasets with controlled properties were employed, and all models were evaluated under a unified training, validation, and replication protocol to ensure comparability and statistical robustness \cite{ref29}.

The experimental design reflects principles commonly adopted in applied biometry, emphasizing reproducibility, controlled variability, and transparent reporting of methodological choices. Rather than prioritizing maximal predictive performance on a single dataset, the focus is placed on understanding performance stability across repeated samples and assessing whether increasingly sophisticated optimization techniques yield practical benefits in realistic healthcare scenarios.

collection particularly well-suited for rigorous comparative evaluation of hyperparameter optimization strategies in healthcare machine learning applications. The comprehensive nature of the data, encompassing diverse demographic and categorical information across both synthetic and real-world contexts, provides a valuable resource for malaria research and modeling efforts.

\subsection{Datasets}

This study employed a comprehensive malaria dataset strategy, combining both synthetically generated data and real clinical records to investigate and model malaria-related symptoms under varying conditions. Five datasets were utilized in the experimental evaluation: four synthetic datasets deliberately generated to exhibit progressively increasing levels of feature interaction and class overlap, and one real clinical dataset obtained from malaria patients. The use of synthetic data alongside real clinical data is a well-established methodological approach in machine learning research, enabling controlled assessment of model behavior under varying degrees of complexity while facilitating the isolation of algorithmic effects from domain-specific noise \cite{ref29}.

\subsubsection{Synthetic Datasets}

The synthetic datasets were designed to represent four distinct complexity scenarios, each comprising 400 observations with 12 features. These scenarios systematically vary coefficient magnitudes, noise levels, and correlation structures to simulate progressively challenging classification tasks:

\begin{enumerate}
\item \textbf{Simple Linear Scenario}: This dataset represents the most straightforward classification task, characterized by clear linear relationships between features and the target variable. Feature correlations are minimal (correlation $\approx$ 0.05), noise levels are low (noise = 0.1), and the decision boundary separating classes is approximately linear. Coefficient magnitudes range from moderate to strong ($|c| \in [0.4, 1.5]$), with minimal feature interactions. This scenario serves as a baseline for assessing fundamental algorithmic performance under ideal conditions where classical linear methods are expected to perform well.

\item \textbf{Complex Nonlinear Scenario}: This dataset introduces moderate complexity through nonlinear feature interactions and stronger dependencies between variables. Feature correlations increase to approximately 0.3, and noise levels rise to 0.2, reflecting more realistic data conditions encountered in clinical settings. Coefficient magnitudes vary ($|c| \in [0.2, 1.2]$) with both positive and negative associations, and nonlinear transformations create curved decision boundaries. This scenario tests algorithms' capacity to capture polynomial and interaction effects that violate linear assumptions, mimicking the complex symptom relationships observed in malaria diagnosis.

\item \textbf{High Noise Scenario}: This dataset emphasizes robustness to measurement error and data quality issues commonly encountered in resource-limited healthcare settings. Substantial noise (noise = 0.5) is introduced while maintaining nonlinear patterns and moderate feature correlations (correlation $\approx$ 0.4). Coefficient magnitudes are attenuated ($|c| \in [0.15, 0.8]$) to reflect signal degradation typical of real-world clinical data where measurement precision may be limited. This scenario evaluates algorithms' stability and generalization capabilities under adverse signal-to-noise conditions characteristic of field diagnostics in malaria-endemic regions.

\item \textbf{Complex Nonlinear - Severe Scenario}: This dataset represents the most challenging synthetic classification task, combining pronounced feature interdependencies (correlation $\approx$ 0.5), moderate noise (noise = 0.3), and strong nonlinear interactions. Coefficient magnitudes vary substantially ($|c| \in [0.2, 1.2]$), creating complex, overlapping decision regions. This scenario approximates the complexity of severe malaria diagnosis where multiple correlated symptoms interact nonlinearly to determine disease severity, closely mimicking the challenges presented by real clinical presentations.
\end{enumerate}

\subsubsection{Correlation Patterns Across Synthetic Datasets}

To understand how dataset complexity affects feature relationships and model behavior, we examined correlation patterns across the four synthetic datasets. Figure~\ref{fig:correlation_matrices} presents Spearman rank correlation matrices for each synthetic dataset, revealing distinct patterns that help explain the performance differences observed in our analyses.

\begin{figure}[htbp]
\centering
\begin{subfigure}{0.48\textwidth}
    \includegraphics[width=\textwidth]{correlation_simple_linear.png}
    \caption{Simple Linear dataset}
    \label{fig:corr_simple}
\end{subfigure}
\hfill
\begin{subfigure}{0.48\textwidth}
    \includegraphics[width=\textwidth]{correlation_simple_linear_severe.png}
    \caption{Simple Linear - Severe dataset}
    \label{fig:corr_simple_severe}
\end{subfigure}

\vspace{0.3cm}

\begin{subfigure}{0.48\textwidth}
    \includegraphics[width=\textwidth]{correlation_complex_nonlinear.png}
    \caption{Complex Nonlinear dataset}
    \label{fig:corr_complex}
\end{subfigure}
\hfill
\begin{subfigure}{0.48\textwidth}
    \includegraphics[width=\textwidth]{correlation_complex_nonlinear_severe.png}
    \caption{Complex Nonlinear - Severe dataset}
    \label{fig:corr_complex_severe}
\end{subfigure}

\caption{Spearman rank correlation matrices across synthetic datasets of increasing complexity}
\label{fig:correlation_matrices}
\end{figure}

The correlation matrices reveal several noteworthy patterns that illuminate the relationship between dataset complexity and model performance. The matrices display progressive increases in feature interdependencies from simple linear relationships to complex nonlinear patterns with severe manifestations, where color intensity indicates correlation strength, with darker blue representing stronger positive correlations. In the Simple Linear dataset (Figure~\ref{fig:corr_simple}), correlations among clinical features are generally weak to moderate, with most values ranging from 0.00 to 0.19. This sparse correlation structure reflects the relatively independent nature of features in this simplified scenario, where relationships follow straightforward linear patterns. The weak interdependencies facilitate model learning, as features provide largely non-redundant information, contributing to the high predictive performance observed for this dataset.

The Simple Linear - Severe variant (Figure~\ref{fig:corr_simple_severe}) introduces slightly stronger correlations, particularly for severe manifestations such as loss of appetite, abdominal pain, and muscle aches. However, the correlation structure remains relatively sparse, with most values still below 0.30. This modest increase in feature interdependence reflects the clinical reality that severe disease presentations often involve multiple correlated symptoms, yet the linear structure is preserved, maintaining model accessibility.

A marked shift occurs in the Complex Nonlinear dataset (Figure~\ref{fig:corr_complex}), where correlation coefficients exhibit substantial increases across the feature space. Values now commonly range from 0.24 to 0.41, with some reaching 0.46. This denser correlation structure indicates stronger feature interactions and nonlinear dependencies that more closely approximate real clinical scenarios where symptoms rarely occur in isolation. Features such as fever, vomiting, fatigue, and headache show moderate to moderately strong intercorrelations, reflecting plausible clinical symptom clusters. The increased interdependence creates a more challenging learning environment, as models must disentangle correlated signals to identify true predictive patterns rather than spurious associations.

The Complex Nonlinear - Severe dataset (Figure~\ref{fig:corr_complex_severe}) exhibits the most pronounced correlation structure, with widespread moderate to strong correlations throughout the matrix. Many feature pairs now demonstrate correlations exceeding 0.40, with some reaching 0.47. This dense interdependency network reflects the complex pathophysiology of severe malaria, where systemic manifestations cascade across multiple organ systems and clinical features co-occur in recognizable patterns \cite{ref5}. The strong correlations among symptoms such as vomiting, fatigue, abdominal pain, and muscle aches mirror clinical observations that severe disease presentations involve multiple concurrent manifestations.

\subsubsection{Feature Relationships in Simple Linear Dataset}

The synthetic datasets were designed to progressively introduce feature interactions and nonlinear relationships, mimicking the transition from simplified diagnostic scenarios to realistic clinical presentations. Figure~\ref{fig:feature_relationships_simple} illustrates the feature correlation structure and distributional properties of the Simple Linear dataset, the least complex synthetic scenario.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.95\textwidth]{image2_feature_relationships.png}
\caption{Feature relationships in the Simple Linear synthetic dataset}
\label{fig:feature_relationships_simple}
\end{figure}

The visualization presents pairwise scatter plots in the off-diagonal positions, marginal distributions along the diagonal, and Spearman correlation coefficients quantifying the strength of monotonic relationships between feature pairs. Features exhibit weak to moderate correlations, with values ranging from -0.232 to 0.183, indicating relatively independent distributions that reduce concerns about multicollinearity. The scatter plots reveal predominantly linear relationships with minimal nonlinear interactions, reflecting the dataset's designed simplicity and alignment with the assumptions underlying linear classification algorithms. Color coding distinguishes Not\_severe (blue) and Severe (purple) malaria cases, demonstrating reasonable class separability in most feature spaces. This sparse correlation structure, combined with clear distributional differences between severity classes, contributed to the high predictive performance observed across all algorithms on this dataset, with F1-scores exceeding 0.85.

The Simple Linear dataset exhibits several characteristics that facilitate model learning. First, the weak to moderate correlations (absolute values typically below 0.25) indicate that features provide largely independent information, reducing multicollinearity concerns that can destabilize linear models \cite{ref29, ref31}. The scatter plots show that most feature pairs exhibit approximately linear relationships with moderate spread, aligning with assumptions underlying algorithms like Logistic Regression and linear Support Vector Machines. Second, the marginal distributions (diagonal histograms) demonstrate reasonable overlap between severity classes across most features, yet with sufficient distributional differences to enable discrimination. For instance, the fever distribution shows higher values concentrated in the severe malaria class (purple), consistent with the clinical observation that hyperpyrexia correlates with parasitemia and disease severity \cite{ref5}. Similarly, vomiting and headache distributions exhibit shifts toward higher values in severe cases, reflecting common clinical manifestations of severe malaria.

Third, the relatively clean separation visible in many scatter plots indicates that even simple decision boundaries can achieve good classification performance. This property explains why simpler algorithms like Logistic Regression performed nearly as well as complex ensemble methods on this dataset, with F1-scores differing by less than 0.05. The absence of complex nonlinear interactions or extreme class overlap reduced the advantage typically conferred by sophisticated algorithms.

\subsubsection{Feature Distribution Comparison Across Datasets}

Figure~\ref{fig:feature_distributions_datasets} extends this analysis by comparing feature distributions across all four synthetic datasets, revealing how increasing complexity affects distributional properties and class separability.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.90\textwidth]{image3_feature_distributions.png}
\caption{Comparison of feature distributions across synthetic datasets of increasing complexity}
\label{fig:feature_distributions_datasets}
\end{figure}

The visualization examines four representative features: fatigue, fever, headache, and vomiting, across the Complex Nonlinear, High Noise, and Simple Linear datasets, with each row representing a dataset and distributions shown separately for Not\_severe (blue) and Severe (purple) malaria cases. The progression across datasets clearly demonstrates how feature complexity affects classification difficulty. In the Simple Linear dataset (bottom row), distributions for severe and not-severe cases show moderate separation with relatively narrow spreads, particularly evident for fever and headache, where distinct peaks and limited overlap enable straightforward classification. As dataset complexity increases from Simple Linear (bottom) to High Noise (middle) to Complex Nonlinear (top), distributional overlap between classes increases substantially and separability decreases correspondingly.

The Complex Nonlinear dataset (top row) exhibits substantially greater distributional overlap compared to simpler scenarios, with wider spreads and less distinct peaks across all examined features. This pattern indicates that symptom values alone provide less discriminative power without considering feature interactions, as the univariate distributions fail to capture the complex, nonlinear relationships that distinguish severe from not-severe cases. The High Noise dataset (middle row) presents an intermediate pattern, with distributional shapes similar to Simple Linear but with notably increased variance reflecting the addition of measurement noise. This variance inflation degrades class separability even when underlying relationships remain relatively simple, underscoring the importance of data quality in predictive modeling \cite{ref25}. The High Noise dataset exhibits the widest distributions and greatest class overlap among all scenarios, reflecting added measurement variability that obscures true signal and complicates accurate classification.

The consistent distributional patterns across features within each dataset validate the synthetic data generation process, ensuring that complexity manipulations affected all features systematically rather than introducing artifacts in specific variables. These distributional differences directly correspond to the performance degradation observed across datasets in our experiments, with F1-scores declining from greater than 0.85 for Simple Linear to approximately 0.73-0.77 for Complex Nonlinear datasets, demonstrating the fundamental constraint that data characteristics impose on achievable model performance.

\subsubsection{Class Distribution Analysis}

Figure~\ref{fig:prevalence_datasets} quantifies the target class distribution across datasets, revealing another dimension of dataset complexity.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.75\textwidth]{image4_prevalence_datasets.png}
\caption{Severe malaria case prevalence across synthetic datasets}
\label{fig:prevalence_datasets}
\end{figure}

All synthetic datasets exhibit similar class distributions, with severe cases comprising 51.2\% to 62.0\% of observations across the four scenarios. This relatively balanced distribution, with all prevalence rates falling within the 40-60\% range, indicates that class imbalance was not a primary driver of performance differences across datasets. The slight variations in prevalence reflect stochastic sampling during synthetic data generation rather than systematic design differences, ensuring that the datasets differ primarily in feature complexity and correlation structure rather than class balance. This consistency in class distribution is methodologically important, as it ensures that performance comparisons across datasets primarily reflect differences in feature complexity and relationships rather than confounding by differential class imbalance.

The relatively balanced class distributions across all synthetic datasets (ranging from 51.2\% to 62.0\% severe cases) represent an important control in the experimental design. By maintaining similar prevalence levels, the study isolated the effects of feature complexity and noise from the confounding influence of class imbalance \cite{ref30}. This design choice ensures that performance differences observed across datasets, with F1-scores declining from greater than 0.85 for Simple Linear to 0.73-0.77 for Complex Nonlinear, primarily reflect algorithmic ability to model feature interactions and handle noise rather than differential sensitivity to class imbalance.

The near-balance in synthetic datasets also contrasts sharply with the real clinical malaria dataset, which exhibited 65.6\% not-severe and 34.4\% severe cases (imbalance ratio approximately 2:1) before balancing interventions. This distinction highlights the additional challenge posed by real-world data, where class imbalance must be explicitly addressed through techniques such as SMOTE \cite{ref30} to achieve acceptable minority class recall. The synthetic datasets' balanced distributions facilitated clearer assessment of how feature complexity affects model performance, independently of class imbalance effects, enabling more precise attribution of performance differences to the intended experimental manipulations.

\subsubsection{Implications for Model Performance}

These progressive increases in correlation strength and density across datasets directly correspond to the performance patterns observed in our experiments. Simple Linear datasets, with their sparse correlation structures, yielded median F1-scores exceeding 0.85, while Complex Nonlinear Severe datasets, characterized by dense interdependencies, produced more modest and variable performance (median F1-scores around 0.73-0.77). This relationship underscores that dataset complexity, as manifested through feature correlation patterns, fundamentally constrains achievable model performance regardless of algorithm sophistication or optimization intensity.

From a methodological perspective, these correlation patterns validate the design of our synthetic datasets as faithful representations of increasing clinical complexity. The progression from weak, sparse correlations to moderate-strong, dense interdependencies mirrors the transition from simplified diagnostic scenarios to realistic clinical presentations where multiple symptoms interact in complex, nonlinear ways. This validation strengthens confidence that performance differences observed across datasets reflect genuine challenges of real-world clinical data rather than artifacts of dataset generation.

The correlation analysis also provides insight into why simple optimization strategies proved sufficient across all datasets. Even in the most complex scenario (Complex Nonlinear - Severe), the correlation structure, while dense, exhibits interpretable patterns rather than chaotic noise. Machine learning algorithms, particularly ensemble methods like Random Forest and gradient boosting approaches like XGBoost, are well-equipped to model such structured complexity through their ability to capture feature interactions and nonlinear relationships \cite{ref32, ref36, ref37}. Once these capable algorithms are selected, hyperparameter optimization contributes relatively little additional benefit because the fundamental challenge, capturing feature interdependencies, is addressed at the algorithmic level rather than through fine-grained parameter tuning.

Importantly, none of the synthetic datasets approached the extreme correlation patterns that might indicate severe multicollinearity or feature redundancy that would necessitate aggressive feature selection or dimensionality reduction. Even in the most complex dataset, no correlation exceeded 0.47, well below thresholds (typically greater than 0.80-0.90) that would indicate problematic multicollinearity requiring intervention \cite{ref29, ref31}. This suggests that in realistic clinical scenarios with moderate feature sets (10-20 variables), careful feature engineering and sophisticated regularization may be less critical than ensuring data quality and selecting appropriate algorithmic families.

\subsubsection{Real Clinical Dataset}

The fifth dataset consisted of real clinical data sourced from a peer-reviewed research article by Awe et al. \cite{awe2025explainable}, who collected comprehensive malaria patient records at the Federal Polytechnic Ilaro Medical Centre, Ilaro, Ogun State, Nigeria. This real-world dataset comprises detailed records of 337 patients who presented with symptoms indicative of malaria over a four-week period, providing a rich source of information for analysis. The patient cohort spans a wide age range, from 3 to 77 years, with an average age of 35.4 years (SD = 14.7). Gender distribution within the dataset shows 180 females and 157 males, indicating a slight gender imbalance. This demographic diversity supports a nuanced analysis of malaria's impact across different age groups and genders. After quality control procedures, 250 complete observations were retained for analysis in the present study.

The clinical dataset includes 16 features representing demographic information and clinical indicators routinely available in healthcare settings. These variables encompass patient age, sex, and various clinical symptoms including fever, cold, rigor, fatigue, headache, bitter tongue, vomiting, diarrhea, convulsion, anemia, jaundice, coca-cola colored urine, hypoglycemia, prostration, and hyperpyrexia. A comprehensive summary of these features is presented in Table~\ref{tab:features}. An exploratory data analysis revealed a class imbalance in the target variable, where 65.6\% of the patients were not diagnosed with severe malaria, while 34.4\% were confirmed to have severe disease. Such an imbalance in the data is a critical consideration, as it can influence the performance of predictive models and necessitates careful handling during model training and evaluation.

\begin{table}[htbp]
\centering
\caption{Description of features in malaria dataset}
\label{tab:features}
\begin{tabular}{@{}ll@{}}
\toprule
\textbf{Feature} & \textbf{Description} \\
\midrule
age & Age of the patient \\
sex & Sex of the patient (1: Male, 0: Female) \\
fever & Presence of fever (1: Yes, 0: No) \\
cold & Presence of cold symptoms (1: Yes, 0: No) \\
rigor & Presence of rigor (shivering) (1: Yes, 0: No) \\
fatigue & Presence of fatigue or tiredness (1: Yes, 0: No) \\
headache & Presence of headache (1: Yes, 0: No) \\
bitter\_tongue & Presence of bitter taste in the mouth (1: Yes, 0: No) \\
vomiting & Presence of vomiting (1: Yes, 0: No) \\
diarrhea & Presence of diarrhea (1: Yes, 0: No) \\
convulsion & Presence of convulsions (seizures) (1: Yes, 0: No) \\
anemia & Reduced red blood cell count or hemoglobin (1: Yes, 0: No) \\
jaundice & Yellowing of skin and eyes (1: Yes, 0: No) \\
cocacola\_urine & Dark-colored urine (1: Yes, 0: No) \\
hypoglycemia & Low blood sugar levels (1: Yes, 0: No) \\
prostration & Extreme weakness or fatigue (1: Yes, 0: No) \\
hyperpyrexia & Extremely high fever (1: Yes, 0: No) \\
\bottomrule
\end{tabular}
\end{table}

\subsubsection{Dataset Integration and Methodological Rationale}

The inclusion of both synthetic and real clinical data serves multiple methodological purposes in this study. The synthetic datasets provide controlled benchmarks for isolating the effects of data complexity, feature interactions, and class separability on model performance, independent of real-world confounds. This controlled environment enables precise attribution of performance differences to specific data characteristics rather than unobserved heterogeneity. The progressive increase in complexity across synthetic scenarios, from simple linear relationships to complex nonlinear interactions with high noise, mirrors the spectrum of challenges encountered when transitioning from idealized experimental conditions to real clinical deployment.

Conversely, the real clinical malaria dataset serves as an implicit benchmark for assessing model performance under authentic deployment conditions, where noise, class imbalance, limited sample size, and patient heterogeneity represent unavoidable challenges \cite{ref1, ref5}. The dataset's characteristics, including class imbalance (65.6\% not severe, 34.4\% severe malaria), complete observations with no missing values, and diverse demographic representation spanning ages 3 to 77 years—make it particularly suitable for evaluating malaria diagnostic models intended for resource-constrained healthcare settings \cite{ref26, ref27, awe2025explainable}.

This dual-dataset strategy enables comprehensive evaluation of how optimization strategies and algorithmic choices interact with both idealized and realistic data conditions. By systematically varying complexity through synthetic scenarios while anchoring findings to real clinical performance, the study provides insights that balance methodological rigour with practical relevance. Performance observed on synthetic datasets establishes upper bounds on achievable accuracy under controlled conditions, while real clinical performance reflects the degradation expected when confronting the irreducible complexity of actual patient data. This approach allows for a more nuanced understanding of which factors, data characteristics, algorithm selection, or optimization strategy, most significantly influence diagnostic performance in malaria prediction.

No additional feature engineering was performed on either synthetic or real datasets, and all variables were retained in their original form to preserve interpretability and reflect realistic deployment conditions. Importantly, all datasets exhibit no missing values, which enhances their reliability and suitability for building robust predictive models. This completeness, combined with the systematic variation in complexity through the synthetic scenarios and the inclusion of the authentic clinical data used in Awe et al. \cite{awe2025explainable}, makes this dataset collection particularly well-suited for rigorous comparative evaluation of hyperparameter optimization strategies in healthcare machine learning applications. The comprehensive nature of the data, encompassing diverse demographic and categorical information across both synthetic and real-world contexts, provides a valuable resource for malaria research and modeling efforts.

Overall, the correlation analysis reinforces the study's central finding: dataset characteristics fundamentally determine achievable performance, with algorithm selection serving as the primary lever for optimization. Hyperparameter tuning and optimization strategy sophistication contribute marginally by comparison. These insights support a pragmatic modeling approach that prioritizes understanding and improving data quality, selecting appropriate algorithms for the complexity at hand, and employing computationally efficient optimization methods that deliver acceptable performance rapidly,  an approach particularly suited to resource-constrained healthcare environments where malaria burden is highest \cite{ref26, ref27}.

\subsection{Data preparation methods}

This section provides a comprehensive overview of the data preprocessing methods utilized in this study to ensure robust and unbiased model training.

\subsubsection{Spearman Rank Correlation Coefficient}

The Spearman Rank Correlation Coefficient, often denoted as $\rho$ or $r_s$, measures the strength and direction of a monotonic relationship between two continuous or ordinal variables. It ranges from $-1$ to $1$, where $r_s = 1$ shows a perfect positive monotonic relationship, $r_s = -1$ shows a perfect negative monotonic relationship, and $r_s = 0$ indicates no monotonic relationship. Understanding the Spearman correlation coefficient is essential for analyzing relationships in our dataset, as it helps identify patterns and associations relevant to malaria-related data, even when relationships are not strictly linear.

The formula for Spearman's correlation is based on the ranks of the data rather than the raw values:

\begin{equation}
r_s = 1 - \frac{6 \sum d_i^2}{n(n^2 - 1)}
\end{equation}

where $d_i$ is the difference between the ranks of each pair of values $(X_i, Y_i)$, and $n$ is the number of data points. In this formula, each variable is ranked from smallest to largest, and the correlation is calculated on these ranks, making Spearman's coefficient more robust for non-linear relationships.

In this study, Spearman Rank Correlation Coefficient analysis was applied to the malaria dataset to assess the relationship between features and the target variable. A correlation matrix was generated to visualize the relationships among all variables. Variables with correlation coefficients close to 1 and $-1$ indicate strong positive and negative correlations, respectively. A threshold of 0.05 was set, and features with correlation coefficients below this threshold were eliminated, which resulted in the removal of 'sex' from the features. As a result, 16 features were retained for further analysis. This approach ensures that only variables with meaningful relationships to the target outcome are included in the modeling process, thereby reducing noise and potential multicollinearity.

\subsubsection{Standardization}

Standardization entails transforming the input data to have zero mean and unit variance. This is crucial in modeling since all inputs are scaled equally, thus avoiding the creation of biased models. Let a dataset contain $n$ observations with $p$ features, $X_j$, $j = 1, 2, \ldots p$, then the mean and standard deviation of feature $j$ can be calculated as follows:

\begin{equation}
\mu_j = \frac{1}{n} \sum_{i=1}^{n} x_i
\end{equation}

\begin{equation}
\sigma_j = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (x_i - \mu_j)^2}
\end{equation}

where $\mu_j$ and $\sigma_j$ are the mean and standard deviation of feature $j$ respectively, $x_i$ is the $i$-th observation in feature $j$, and $n$ is the total observations. Standardization of an observation $i$ for feature $j$ using z-score normalization can be given by:

\begin{equation}
X_{\text{standardized}} = \frac{x_i - \mu_j}{\sigma_j}
\end{equation}

Standardization is an important technique in machine learning that helps improve the robustness and generalizability of models. In this study, we standardized our data to ensure the data was on the same scale and for consistent results across the models used. Continuous variables were standardized prior to model training, while categorical variables were encoded using appropriate binary representations.

\subsubsection{Handling class imbalance}

Class imbalance is a common characteristic of clinical datasets and poses significant challenges for classification models, particularly when minority-class detection is of primary clinical interest \cite{ref30}. In the present study, an exploratory data analysis of the real clinical malaria dataset \cite{awe2025explainable} revealed a class imbalance in the target variable, where 65.6\% of the patients were not diagnosed with severe malaria, while 34.4\% were confirmed to have severe disease. Such an imbalance in the data is a critical consideration, as it can influence the performance of predictive models. The imbalance ratio of the clinical dataset before balancing was approximately 1:2, meaning that for every severe malaria patient, there were approximately two non-severe patients. The highly imbalanced nature of the real clinical data, therefore, made it imperative for balancing to be carried out. Notably, the synthetic datasets were deliberately generated with relatively balanced class distributions to isolate the effects of feature complexity and noise from confounding by class imbalance.

In the present study, imbalance in the real clinical dataset was addressed exclusively within the training data using oversampling techniques, thereby avoiding information leakage into validation folds. This approach aligns with best practices in applied statistics and machine learning, ensuring that performance estimates remain unbiased. Synthetic Minority Over-sampling Technique (SMOTE)–based procedures \cite{ref30} were employed to generate additional synthetic samples for the minority class by interpolating between nearest neighbors in feature space.

Over-sampling is a technique used in machine learning to aid in addressing class imbalance. The minority class will be enhanced by this way of replicating existing instances and making sure that each category has equal number of samples. This method functions very much like KNN. Considering $X$ to be the input matrix having minority class instances, $k$ being the number of nearest neighbors to be considered and $m$ as the synthetic samples to generate. Let $x_i$ represent an observation on a minority data point $x_{ij}$ which is the $i$th observation on $j$th feature and $k$ randomly selected neighbors. The new feature vector, $X_{i,\text{new}}$, is defined as:

\begin{equation}
X_{j,\text{new}} = X_j + [\alpha(X_j - X_r)]
\end{equation}

where $X_j$ is the original feature vector, $\alpha$ is any random number between 0 and 1, while $X_r$ denotes a randomly chosen feature vector from all available vectors. Overfitting observed in random sampling can be mitigated through oversampling. Classification accuracy can improve if this technique is used.

Oversampling was applied only within each training fold during cross-validation, and the validation data were left unaltered. This strategy preserves the original class distribution in the evaluation phase and allows meaningful assessment of diagnostic performance under realistic prevalence conditions. We balanced the train set instead of the entire dataset to reduce the chances of overfitting. Other methods, such as synthetic data generation beyond SMOTE, were not considered because the dataset involved sensitive medical data, where additional synthetic data generation could introduce risks of inaccuracies or distortions that might compromise the integrity of the study.

Model performance was primarily assessed using the F1-score, which balances precision and recall and is particularly appropriate for imbalanced classification problems. Accuracy was not emphasized as the primary metric, as it can be misleading when class proportions are skewed. However, we also evaluated models using a comprehensive set of metrics including accuracy, balanced accuracy, Matthews Correlation Coefficient (MCC), Cohen's Kappa, precision, recall, and specificity to provide a holistic view of model performance.

\subsection{Machine Learning Models}

A diverse set of machine learning models were evaluated to represent a broad spectrum of algorithmic approaches. This section provides mathematical formulations for each model employed in the study.

\subsubsection{Logistic Regression}

Logistic Regression (LR) is a probabilistic linear classifier widely used in clinical prediction due to its interpretability and statistical grounding. The model estimates the conditional probability of class membership given an input feature vector by applying the logistic function to a linear combination of predictors.

Formally, the probability of observing class $y=1$ given predictors $x \in \mathbb{R}^p$ is defined as:

\begin{equation}
P(y=1|x) = \frac{1}{1 + \exp(-(\beta_0 + \beta^\top x))}
\end{equation}

where $\beta_0$ is the intercept and $\beta$ is the vector of regression coefficients. Model parameters are estimated by maximizing the penalized log-likelihood \cite{ref31}:

\begin{equation}
L(\beta) = \sum_{i=1}^{n} [y_i \log(p_i) + (1 - y_i)\log(1 - p_i)] - \lambda\|\beta\|^q
\end{equation}

where $\lambda$ controls regularization strength and $q \in \{1,2\}$ corresponds to L1 (lasso) or L2 (ridge) penalties. Regularization is critical in clinical datasets to mitigate multicollinearity and overfitting, particularly when sample sizes are limited.

\subsubsection{Random Forest}

Random Forest (RF) is an ensemble learning method that aggregates predictions from multiple decision trees constructed on bootstrapped samples of the data. Each tree partitions the feature space through recursive binary splits that maximize impurity reduction.

For classification, impurity at a node $t$ is commonly measured using the Gini index:

\begin{equation}
G(t) = 1 - \sum_{k=1}^{K} p_k^2
\end{equation}

where $p_k$ is the proportion of observations of class $k$ in node $t$. At each split, a random subset of predictors is considered, introducing decorrelation among trees. Final predictions are obtained via majority voting:

\begin{equation}
\hat{y} = \text{mode}\{h_1(x), \ldots, h_B(x)\}
\end{equation}

where $h_b$ denotes the $b$-th tree \cite{ref32}. This structure yields robustness to noise and nonlinear interactions, though at the cost of reduced interpretability compared to linear models. The basic idea of RF is to enhance the bagging variance by reducing the correlation between trees. This objective is accomplished during the tree-building process by randomly selecting input variables. Every node is divided from a subset of predictors chosen arbitrarily at every node into the best predictors. Prior to every split, RF chooses arbitrarily $b \leq a$ input variables as candidates for splitting where $a$ is the overall number of input variables. Most of the time, $b$ has a value of $\sqrt{a}$ or possibly just 1. Additionally, trees with particular framework qualities are produced by this choice at random.

\subsubsection{Support Vector Machine}

Support Vector Machines (SVM) aim to construct a decision boundary that maximizes the margin between classes in a transformed feature space. Given training data $(x_i, y_i)$, the primal optimization problem is:

\begin{equation}
\min_{w,\xi} \frac{1}{2}\|w\|^2 + C \sum_{i=1}^{n} \xi_i
\end{equation}

subject to:

\begin{equation}
y_i(w^\top\phi(x_i) + b) \geq 1 - \xi_i, \quad \xi_i \geq 0
\end{equation}

where $\phi(\cdot)$ denotes a feature mapping induced by a kernel function. In this study, the radial basis function kernel was employed:

\begin{equation}
K(x_i, x_j) = \exp(-\gamma\|x_i - x_j\|^2)
\end{equation}

SVMs are particularly effective in high-dimensional spaces and demonstrate strong generalization properties, making them well-suited for clinical classification tasks \cite{ref33, ref34}. The hyperparameter $C$ controls the trade-off between maximizing the margin and minimizing the classification error, while $\gamma$ determines the influence of individual training examples.

\subsubsection{Neural Network}

The Neural Network model employed consists of a single hidden layer feedforward architecture. Given input $x$, the hidden layer activation is computed as:

\begin{equation}
h = \sigma(W_1x + b_1)
\end{equation}

where $\sigma(\cdot)$ denotes the sigmoid activation function. The output layer produces class probabilities via:

\begin{equation}
\hat{y} = \sigma(W_2h + b_2)
\end{equation}

Model training minimizes the cross-entropy loss function with regularization:

\begin{equation}
L = -\sum_{i=1}^{n} [y_i \log(\hat{y}_i) + (1 - y_i)\log(1 - \hat{y}_i)] + \lambda\|\theta\|^2
\end{equation}

Neural Networks offer high representational capacity, enabling modeling of complex nonlinear relationships present in clinical data \cite{ref35}, albeit with increased sensitivity to hyperparameter selection. The regularization term $\lambda\|\theta\|^2$ helps prevent overfitting by penalizing large weight values.

\subsubsection{XGBoost}

Extreme Gradient Boosting (XGBoost) constructs additive tree-based models by sequentially fitting weak learners to the residuals of previous iterations. The objective function is:

\begin{equation}
L^{(t)} = \sum_{i=1}^{n} l(y_i, \hat{y}_i^{(t-1)} + f_t(x_i)) + \Omega(f_t)
\end{equation}

where $l(\cdot)$ is a differentiable loss function and $\Omega(f) = \gamma T + \frac{1}{2}\lambda\|w\|^2$ penalizes model complexity \cite{ref36, ref37}. This regularization framework enhances generalization and computational efficiency. XGBoost is built similarly to Gradient Boosting as an objective function is expanded additively through the minimization of the loss function. It is used for supervised learning tasks, such as regression and classification.

The algorithm works by sequentially adding weak learners to the ensemble, with each new learner focusing on correcting the errors made by the existing ones. It uses a gradient descent optimization technique to minimize a predefined loss function during training. The gradient boosting is then used to efficiently solve the classification problem with loss function and extended by second-order Taylor expansion. The optimal weight $w_j^*$ of leaf $j$ can be calculated, and a scoring function that measures the quality of tree structure can be derived. This function provides a principled way to evaluate different tree structures during the greedy tree construction process.

\subsubsection{K-Nearest Neighbors}

K-Nearest Neighbors (KNN) is a non-parametric classifier that assigns class labels based on proximity in feature space. For a query point $x$, prediction is given by:

\begin{equation}
\hat{y} = \arg\max_c \sum_{i \in N_k(x)} I(y_i = c)
\end{equation}

where $N_k(x)$ denotes the set of $k$ nearest neighbors under a chosen distance metric, typically Euclidean distance \cite{ref38}. Despite its simplicity, KNN can perform competitively when feature scaling is appropriate and noise levels are moderate. The choice of $k$ is critical: small values of $k$ can lead to overfitting and sensitivity to noise, while large values may oversmooth decision boundaries and reduce classification accuracy.

\subsection{Hyperparameter optimization strategies}

Two broad categories of hyperparameter optimization strategies were evaluated in this study: stochastic and deterministic methods. Stochastic approaches included Random Search \cite{ref20}, Genetic Algorithms \cite{ref23}, and Hyperband Racing \cite{ref24}, while deterministic methods comprised Grid Search and Bayesian Optimization \cite{ref22}. For fairness, identical hyperparameter search spaces were defined across methods, and computational budgets were constrained to reflect realistic conditions. Random Search \cite{ref20} samples hyperparameter configurations uniformly at random, offering efficient exploration in high-dimensional spaces. This approach has been shown to be particularly effective when only a subset of hyperparameters substantially influences model performance, as it allocates computational resources more efficiently than exhaustive grid-based approaches. Grid Search evaluates all combinations in a predefined grid but can be computationally expensive, especially in high-dimensional parameter spaces. Despite this limitation, it remains popular due to its simplicity and guaranteed coverage of the search space.

Bayesian Optimization \cite{ref22} constructs a probabilistic surrogate model of the objective function and selects new configurations based on acquisition functions. This method balances exploration of uncertain regions with exploitation of promising configurations, potentially requiring fewer evaluations than random or grid search to identify optimal hyperparameters. Genetic Algorithms \cite{ref23} evolve populations of candidate solutions through selection, crossover, and mutation operations inspired by biological evolution. These methods can effectively explore complex, non-convex search spaces but may require careful tuning of their own meta-parameters. Hyperband \cite{ref24} allocates resources adaptively using early-stopping criteria, rapidly eliminating poorly performing configurations and focusing computational effort on more promising candidates. This approach can be particularly efficient when evaluations are expensive and partial evaluations provide informative signals about final performance.

\subsection{Model training and validation}

Model evaluation was conducted using 10-fold cross-validation repeated five times, yielding robust performance estimates and enabling variance decomposition analyses \cite{ref29}. For each algorithm–optimization combination, five independent replications were performed. Hyperparameter optimization was restricted to training folds within each repetition, ensuring strict separation between training and validation data. This rigorous evaluation protocol minimizes the risk of overfitting to specific data splits and provides reliable estimates of generalization performance.

All analyses were implemented in the R statistical environment, leveraging established machine learning libraries to ensure reproducibility. Computational efficiency was quantified as the number of hyperparameter evaluations per minute, providing a practical measure of optimization cost. This metric is particularly relevant for resource-constrained healthcare settings where computational infrastructure may be limited \cite{ref26, ref27}.

\section{Results and Discussion}

\subsection{Overall Performance of Optimization Strategies}

Table~\ref{tab:optimization_summary} presents a comprehensive summary of optimization performance comparing stochastic and deterministic approaches across all experiments.

\begin{table}[ht]
\centering
\caption{Summary of optimization performance by type}
\label{tab:optimization_summary}
\begin{tabular}{@{}lcccccccc@{}}
\toprule
\textbf{Type} & \textbf{n\_exp} & \textbf{mean\_f1} & \textbf{sd\_f1} & \textbf{mean\_acc} & \textbf{sd\_acc} & \textbf{mean\_roc} & \textbf{mean\_time} \\
\midrule
Stochastic & 72 & 0.7834 & 0.0515 & 0.7496 & 0.0640 & 0.8262 & 11.58 \\
Deterministic & 48 & 0.7833 & 0.0498 & 0.7495 & 0.0621 & 0.8281 & 2.51 \\
\bottomrule
\end{tabular}
\end{table}

The results reveal striking consistency in predictive performance between stochastic and deterministic methods, with mean F1-scores of 0.7834 and 0.7833 respectively—a difference of less than 0.01\%. However, deterministic methods demonstrated substantially superior computational efficiency, with mean training time of 2.51 minutes compared to 11.58 minutes for stochastic methods, representing a 4.6-fold speed advantage.

Table~\ref{tab:method_comparison} provides detailed performance metrics for each optimization method, stratified by optimization type.

\begin{table}[ht]
\centering
\caption{Detailed comparison of optimization methods}
\label{tab:method_comparison}
\small
\begin{tabular}{@{}llccccc@{}}
\toprule
\textbf{Method} & \textbf{Type} & \textbf{n\_exp} & \textbf{mean\_f1} & \textbf{sd\_f1} & \textbf{mean\_acc} & \textbf{mean\_time} & \textbf{efficiency} \\
\midrule
Hyperband Racing & Stochastic & 24 & 0.7841 & 0.0532 & 0.7496 & 3.20 & 0.245 \\
Bayesian Opt. & Deterministic & 24 & 0.7839 & 0.0510 & 0.7484 & 3.14 & 0.249 \\
Genetic Alg. & Stochastic & 24 & 0.7831 & 0.0571 & 0.7500 & 29.18 & 0.027 \\
Random Search & Stochastic & 24 & 0.7830 & 0.0456 & 0.7491 & 2.36 & 0.332 \\
Grid Search & Deterministic & 24 & 0.7827 & 0.0497 & 0.7507 & 1.88 & 0.416 \\
\bottomrule
\end{tabular}
\end{table}

The detailed comparison reveals that Grid Search achieved the highest computational efficiency (0.416 evaluations/minute) despite being a deterministic exhaustive method, followed by Random Search (0.332). In stark contrast, Genetic Algorithms exhibited the lowest efficiency (0.027), requiring nearly 30 minutes on average—over 15 times longer than Grid Search—without any compensating performance advantage. Remarkably, all methods achieved nearly identical mean F1-scores (ranging from 0.7827 to 0.7841), with differences well within one standard deviation.

The correlation matrix reveals several important patterns that inform our understanding of hyperparameter optimization in the malaria classification context. First, strong positive correlations are observed among the primary performance metrics—test accuracy, test precision, test F1-score, and test ROC AUC—with correlation coefficients ranging from 0.85 to 1.0. This high intercorrelation suggests that models performing well on one metric tend to perform well across all metrics, indicating consistent predictive quality rather than metric-specific optimization artifacts. The particularly strong correlation between test precision and test ROC AUC ($r = 0.97$) underscores the alignment between these metrics in capturing model discriminative ability.

Interestingly, test recall shows a somewhat different pattern, exhibiting strong positive correlation with test F1-score ($r = 1.0$) as expected given the mathematical relationship between these metrics, but showing weaker and even slightly negative correlations with test specificity ($r = -0.47$). This inverse relationship between recall and specificity reflects the fundamental trade-off in classification thresholds: optimizing for sensitivity (recall) often comes at the expense of specificity, and vice versa. This trade-off is particularly relevant in clinical contexts where the costs of false positives and false negatives may differ substantially.

The number of evaluations (n\_evaluations) shows near-perfect positive correlation with itself ($r = 1.0$) across the diagonal, as expected, but demonstrates minimal correlation with most performance metrics. The correlation between n\_evaluations and test accuracy is essentially zero ($r = 0.0$), and similarly negligible correlations are observed with test precision ($r = 0.0$), test F1-score ($r = 0.0$), and test ROC AUC ($r = 0.0$). This pattern provides early evidence that simply increasing the number of hyperparameter evaluations does not guarantee improved model performance, supporting the hypothesis that diminishing returns exist beyond a modest evaluation budget.

Efficiency score shows strong negative correlation with training time in minutes ($r = -0.31$), which is consistent with the definition of efficiency as evaluations per unit time. Methods that complete more evaluations per minute naturally achieve higher efficiency scores. Notably, efficiency score shows minimal correlation with most performance metrics (correlations near zero), suggesting that computational efficiency and predictive performance are largely orthogonal concerns in this experimental context. This independence has important practical implications: practitioners can prioritize computational efficiency without necessarily sacrificing model quality.

Training time in minutes exhibits a strong positive correlation with n\_evaluations ($r = 0.9$), indicating that optimization methods requiring more evaluations naturally consume more time. However, the weak correlation between training time and performance metrics (e.g., correlation with test accuracy $r = 0.0$) reinforces the conclusion that longer optimization runs do not consistently yield better models. The slight negative correlation between training time and test specificity ($r = -0.11$) may suggest that prolonged optimization occasionally leads to overfitting on the majority class in imbalanced datasets.

Test specificity shows moderate positive correlations with test accuracy ($r = 0.69$), test precision ($r = 0.76$), and test ROC AUC ($r = 0.76$), indicating that models with good overall performance tend to correctly identify negative cases. However, its negative correlation with test recall ($r = -0.47$) highlights the inherent tension between sensitivity and specificity that must be balanced in clinical applications.

Overall, the correlation analysis provides quantitative support for several key findings: (1) performance metrics are highly intercorrelated, suggesting robust model quality rather than metric-specific artifacts; (2) computational effort (measured by n\_evaluations or training time) shows minimal correlation with performance, indicating diminishing returns; (3) efficiency and performance are largely independent, allowing practitioners to prioritize computational parsimony; and (4) the recall-specificity trade-off is evident and must be explicitly managed in imbalanced clinical datasets.

\subsection{Performance Before and After Class Balancing}

Model performance was comprehensively assessed using multiple evaluation metrics including accuracy, precision, recall, F1-score, balanced accuracy, Matthews Correlation Coefficient (MCC), Cohen's Kappa, and specificity. Prior to class balancing, several models achieved high accuracy but exhibited reduced recall for malaria-positive cases, indicating bias toward the majority class. This pattern is typical in imbalanced classification scenarios where models can achieve superficially high accuracy by predominantly predicting the majority class.

\begin{table}[ht]
\centering
\caption{Performance evaluation metric results before balancing}
\label{tab:before_balance}
\begin{tabular}{@{}lcccccccc@{}}
\toprule
\textbf{Model} & \textbf{Accuracy} & \textbf{ROC AUC} & \textbf{MCC} & \textbf{B. Acc} & \textbf{Cohen's K.} & \textbf{Precision} & \textbf{Recall} & \textbf{F1 Score} \\
\midrule
Random F. & 0.647 & 0.580 & 0.140 & 0.548 & 0.113 & 0.538 & 0.189 & 0.280 \\
Neural Net & 0.637 & 0.592 & 0.132 & 0.552 & 0.118 & 0.500 & 0.243 & 0.327 \\
SVM & 0.627 & 0.567 & 0.100 & 0.539 & 0.088 & 0.471 & 0.216 & 0.296 \\
Log. Reg. & 0.618 & 0.598 & 0.090 & 0.537 & 0.082 & 0.450 & 0.243 & 0.316 \\
XGBoost & 0.588 & 0.561 & 0.078 & 0.537 & 0.077 & 0.419 & 0.351 & 0.382 \\
KNN & 0.598 & 0.571 & 0.088 & 0.542 & 0.085 & 0.435 & 0.265 & 0.330 \\
\bottomrule
\end{tabular}
\end{table}

As revealed in Table 4, the performance metrics before balancing reveal several important patterns. While the Random Forest model achieves the highest accuracy score (64.7\%), it struggles with balanced accuracy (54.8\%) and MCC (0.140), indicating challenges in correctly identifying true negatives. The large gap between accuracy (0.647) and balanced accuracy (0.548) demonstrates the model's bias toward the majority class. The extremely low recall (0.189) is particularly concerning from a clinical perspective, as it indicates that the model fails to identify approximately 81\% of malaria-positive cases. This high false negative rate would be unacceptable in clinical practice, where missing malaria diagnoses can lead to severe complications and mortality \cite{ref5}.

Neural Networks follow closely with slightly lower accuracy (63.7\%) but exhibit comparable balanced accuracy (55.2\%) and MCC (0.132), showcasing similar overall performance in handling the imbalanced dataset. While Neural Networks show improved recall (0.243) compared to Random Forest, this still represents missing approximately 76\% of positive cases, highlighting the pervasive impact of class imbalance on model behavior.

Support Vector Machines, Logistic Regression, and KNN models also face difficulties in balanced accuracy and MCC, indicating similar struggles in true negative identification. XGBoost shows lower overall performance metrics, with accuracy of 58.8\% and MCC of 0.078 among the models. Interestingly, XGBoost exhibits relatively higher recall (0.351) and F1 score (0.382) than other models, suggesting better identification of positive instances despite lower overall accuracy. This pattern may reflect XGBoost's sequential learning process, which can be more robust to class imbalance than single-pass learning algorithms.

The confusion matrix analysis prior to balancing revealed that all models struggled to correctly identify the true negative (TN) classes effectively. Out of the true negative cases in the test dataset, models consistently exhibited low true negative rates, instead misclassifying many negative cases as positive (false positives). More critically, the false negative rates were alarmingly high across all models, with Random Forest missing 81\% of positive cases, Neural Networks missing 76\%, and even the best performer (XGBoost) missing 65\% of malaria cases. This pattern underscores the necessity of incorporating balancing techniques in the study to improve model performance on both classes, but particularly on the minority class where clinical consequences of misclassification are most severe.

After applying over-sampling techniques using SMOTE \cite{ref30}, recall and F1-score improved consistently across most models, demonstrating enhanced detection of positive cases. The improvement was particularly pronounced for ensemble-based models such as Random Forests and Neural Networks, which showed substantial increases in their ability to correctly identify malaria-positive cases.

\begin{table}[ht]
\centering
\caption{Performance evaluation metric results after balancing}
\label{tab:after_balance}
\begin{tabular}{@{}lcccccccc@{}}
\toprule
\textbf{Model} & \textbf{Accuracy} & \textbf{ROC AUC} & \textbf{MCC} & \textbf{B. Acc} & \textbf{Cohen's K.} & \textbf{Precision} & \textbf{Recall} & \textbf{F1 Score} \\
\midrule
Random F. & 0.767 & 0.853 & 0.532 & 0.766 & 0.532 & 0.786 & 0.775 & 0.780 \\
Neural Net & 0.767 & 0.821 & 0.532 & 0.766 & 0.532 & 0.786 & 0.774 & 0.780 \\
SVM & 0.737 & 0.787 & 0.470 & 0.733 & 0.469 & 0.737 & 0.789 & 0.762 \\
Log. Reg. & 0.722 & 0.803 & 0.439 & 0.718 & 0.438 & 0.724 & 0.775 & 0.748 \\
XGBoost & 0.722 & 0.803 & 0.439 & 0.718 & 0.438 & 0.724 & 0.775 & 0.748 \\
KNN & 0.617 & 0.675 & 0.230 & 0.615 & 0.230 & 0.643 & 0.634 & 0.638 \\
\bottomrule
\end{tabular}
\end{table}

Results in Table 5 show that after implementing oversampling techniques to handle class imbalance in the malaria dataset, significant improvements were observed in the performance metrics of various machine-learning models. Both the Random Forest and Neural Network models exhibited substantial increases in accuracy scores, reaching 76.7\%, representing improvements of 12 and 13 percentage points, respectively. More importantly, recall improved dramatically from 0.189 to 0.775 for Random Forest (a 310\% increase) and from 0.243 to 0.774 for Neural Networks (a 218\% increase). These improvements in recall are clinically critical, as they represent a reduction in missed malaria diagnoses from 81\% to 22.5\% for Random Forest and from 76\% to 22.6\% for Neural Networks.

The ROC-AUC scores also showed remarkable improvement, with Random Forest achieving 0.853 (up from 0.580) and Neural Networks reaching 0.821 (up from 0.592). These substantial improvements in AUC indicate enhanced discriminative ability across all classification thresholds. The Matthews Correlation Coefficient [29], which provides a balanced measure accounting for all confusion matrix elements, increased from 0.140 to 0.532 for Random Forest and from 0.132 to 0.532 for Neural Networks, indicating a transformation from weak to moderate-strong prediction quality.

The alignment between balanced accuracy and overall accuracy after SMOTE application (0.766 vs 0.767 for both Random Forest and Neural Networks) demonstrates that the models are no longer biased toward the majority class. This balance is essential for clinical deployment, where both sensitivity and specificity matter for effective diagnosis and resource allocation.

Support Vector Machines, Logistic Regression, and XGBoost also showed notable improvements across most metrics. SVM achieved 73.7\% an accuracy with strong recall (0.789) and ROC AUC of 0.787. Logistic Regression and XGBoost both reached 72.2\% accuracy with recall of 0.775 and ROC AUC of 0.803, demonstrating solid performance though slightly below the top performers. The improvement for XGBoost was more modest compared to other models, likely because its sequential boosting process already provided some robustness to class imbalance even before explicit balancing.

However, the KNN model, while showing some improvements post-oversampling, still lagged behind significantly in all performance metrics compared to the other models. With accuracy of 61.7\%, MCC of 0.230, and ROC AUC of 0.675, KNN demonstrated fundamental limitations in this clinical classification task. The relatively poor performance of KNN can be attributed to its sensitivity to class imbalance, reliance on distance metrics that may not capture complex symptom interactions, and lack of feature weighting mechanisms emphasize clinically important variables.

\subsection{Confusion Matrix Analyses}

Confusion matrix analysis provides detailed insights into the classification performance of each model, revealing the specific types of errors made and their clinical implications. Before balancing, confusion matrices revealed a substantial number of false negatives, indicating missed malaria diagnoses. This is clinically significant, as false negatives correspond to patients with malaria who would not receive appropriate treatment, potentially leading to disease progression, severe complications, and continued transmission within communities \cite{ref5}.

After applying SMOTE-based oversampling \cite{ref30}, confusion matrices showed notable improvements in true positive (TP) and true negative (TN) identification for all the ensemble machine learning models in the malaria dataset. Specifically, both the Random Forest and Neural Network models showed enhanced TP and TN rates, indicating improved accuracy in identifying both malaria and non-malaria cases. For Random Forest, true positives increased from approximately 19\% of actual positive cases to 77.5\%, while maintaining reasonable true negative rates. Similarly, Neural Networks improved from 24.3\% to 77.4\% true positive rate.

The substantial reduction in false negatives following class balancing is particularly important from a clinical perspective, as it directly translates to fewer missed diagnoses. For instance, in a cohort of 100 malaria-positive patients, the pre-balancing Random Forest model would miss approximately 81 cases, while the post-balancing model would miss only 22-23 cases—a reduction of over 70\% in missed diagnoses. This improvement could translate to significant reductions in morbidity and mortality in clinical practice.

Although a modest increase in false positives was observed following SMOTE application, the overall trade-off favors improved patient safety. The increase in false positive rate from approximately 35\% to 21-23\% (i.e., a reduction in true negative rate from 65\% to 77-79\%) represents a favorable exchange: fewer missed malaria cases at the cost of some additional confirmatory testing for false positives. In clinical practice, the consequences of missing a malaria diagnosis (false negative) are generally more severe than those of a false positive, which would prompt further confirmatory testing through microscopy or PCR but would not result in untreated infection \cite{ref6, ref7}.

The confusion matrices also revealed model-specific patterns. Random Forest and Neural Networks showed the most balanced performance across both classes, with similar true positive and true negative rates. Support Vector Machines demonstrated slightly higher recall (78.9\%) but marginally lower precision (73.7\%), reflecting a more liberal classification threshold. Logistic Regression and XGBoost showed identical confusion patterns with balanced performance across metrics. KNN exhibited the weakest performance with notably higher error rates in both false positives and false negatives, confirming its limitations for this classification task.

\subsection{Comparative Analysis of Algorithm Performance}

To illustrate the practical implications of algorithm selection on diagnostic performance, we present a detailed comparison of confusion matrices for representative algorithms. Figure~\ref{fig:confusion_comparison} displays confusion matrices for Random Forest and Logistic Regression on the clinical malaria dataset after class balancing and hyperparameter optimization.

\begin{figure}[ht]
\centering
\includegraphics[width=0.95\textwidth]{image1_confusion_matrices.png}
\caption{Confusion matrix comparison between Random Forest (left) and Logistic Regression (right) models on the malaria dataset. Random Forest achieved superior true positive rate (90.3\%) and true negative rate (90.2\%), with only 9.7\% false negatives and 9.8\% false positives. Logistic Regression showed comparatively higher false negative rate (15.4\%), resulting in more missed malaria diagnoses. The cell counts and percentages demonstrate Random Forest's more balanced performance across both classes, critical for clinical deployment where both sensitivity and specificity matter.}
\label{fig:confusion_comparison}
\end{figure}

The confusion matrix analysis reveals substantial differences in classification patterns between algorithms. Random Forest correctly identified 185 of 205 severe malaria cases (true positives), missing only 20 cases (9.7\% false negative rate). In contrast, Logistic Regression missed 30 cases (15.4\% false negative rate), representing a 50\% increase in missed diagnoses compared to Random Forest. From a clinical perspective, this difference is highly significant: in a cohort of 1,000 malaria-positive patients, Random Forest would miss approximately 97 cases while Logistic Regression would miss 154 cases—a difference of 57 additional missed diagnoses that could result in delayed treatment and potential complications \cite{ref5}.

The true negative rates also differed meaningfully, with Random Forest achieving 90.2\% specificity compared to Logistic Regression's 85.9\%. While both algorithms maintained reasonably high specificity, Random Forest's 4.3 percentage point advantage translates to fewer false positives and reduced unnecessary confirmatory testing. In resource-constrained settings where confirmatory testing capacity is limited \cite{ref26,ref27}, this reduction in false positives can meaningfully improve healthcare efficiency without compromising sensitivity.

These performance differences reflect fundamental algorithmic properties. Random Forest's ensemble approach, combining multiple decision trees trained on bootstrapped samples with random feature subsets \cite{ref32}, enables robust capture of complex, nonlinear symptom interactions characteristic of malaria presentation. The model's implicit feature selection mechanism—where only the most informative features are used for splitting at each node—reduces susceptibility to noisy or irrelevant predictors. Logistic Regression, while highly interpretable and computationally efficient, assumes linear relationships between log-odds and predictors \cite{ref31}, a constraint that may be violated by the complex pathophysiology of severe malaria where symptom interactions exhibit nonlinear patterns \cite{ref5}.

\subsection{Hyperparameter Tuning and Optimization}

To further enhance model performance beyond the gains achieved through class balancing, systematic hyperparameter tuning was conducted for all models. We employed RandomizedSearchCV \cite{ref20} with 5-fold cross-validation to identify optimal hyperparameter configurations while maintaining computational efficiency. The search strategy balanced exploration of the hyperparameter space with practical constraints on computational budget.

For Random Forest, we tuned the number of trees (n\_estimators) exploring values from 50 to 500, maximum depth (max\_depth) from 5 to 50, minimum samples split (min\_samples\_split) from 2 to 20, minimum samples leaf (min\_samples\_leaf) from 1 to 10, and the maximum number of features (max\_features) considering 'sqrt', 'log2', and None options. The optimization process evaluated 50 configurations over 20 candidates, ultimately identifying an optimal configuration with n\_estimators=300, max\_depth=30, min\_samples\_split=5, min\_samples\_leaf=2, and max\_features='sqrt'.

For Neural Networks, hyperparameter tuning focused on hidden layer sizes exploring architectures from (10,) to (200, 100, 50), activation functions ('relu', 'tanh', 'logistic'), learning rate initialization (0.0001 to 0.1), regularization parameter alpha (0.0001 to 0.1), and learning rate schedules ('constant', 'adaptive'). The search identified optimal configurations favoring moderate network complexity with hidden\_layer\_sizes=(100, 50), activation='relu', learning\_rate\_init=0.001, and alpha=0.01.

Support Vector Machines were tuned across regularization parameter C (0.1 to 100), kernel coefficient gamma (0.001 to 1.0), and kernel types ('rbf', 'linear', 'poly'). The optimization identified C=10, gamma=0.1, and kernel='rbf' as the optimal configuration, balancing model complexity with generalization (see Figure~\ref{fig:bayesian_svm}).

For Logistic Regression, we explored regularization strength C (0.01 to 100), penalty types ('l1', 'l2', 'elasticnet'), and solvers ('liblinear', 'saga', 'lbfgs'). The optimal configuration combined moderate regularization (C=1.0) with L2 penalty and 'lbfgs' solver.

XGBoost hyperparameter tuning examined number of estimators (50 to 500), learning rate (0.01 to 0.3), maximum depth (3 to 15), minimum child weight (1 to 10), subsample ratio (0.6 to 1.0), and column sample by tree (0.6 to 1.0). The optimization identified n\_estimators=200, learning\_rate=0.1, max\_depth=6, min\_child\_weight=3, subsample=0.8, and colsample\_bytree=0.8 as optimal (see Figure~\ref{fig:bayesian_xgboost}).

KNN tuning focused on number of neighbors (3 to 50), distance metrics ('euclidean', 'manhattan', 'minkowski'), and weighting schemes ('uniform', 'distance'). The optimal configuration used n\_neighbors=7, metric='euclidean', and weights='distance'.

\begin{figure}[ht]
\centering
\begin{subfigure}{0.48\textwidth}
    \includegraphics[width=\textwidth]{image10_bayesian_xgboost.png}
    \caption{XGBoost hyperparameter exploration}
    \label{fig:bayesian_xgboost}
\end{subfigure}
\hfill
\begin{subfigure}{0.48\textwidth}
    \includegraphics[width=\textwidth]{image11_bayesian_svm.png}
    \caption{SVM hyperparameter exploration}
    \label{fig:bayesian_svm}
\end{subfigure}
\caption{Bayesian Optimization exploration of hyperparameter spaces for (a) XGBoost and (b) SVM models, showing the distribution of evaluated configurations and their corresponding performance across different parameter combinations.}
\label{fig:bayesian_exploration}
\end{figure}

\begin{table}[ht]
\centering
\caption{Model performance after hyperparameter tuning}
\label{tab:after_tuning}
\begin{tabular}{@{}lcccccccc@{}}
\toprule
\textbf{Model} & \textbf{Accuracy} & \textbf{ROC AUC} & \textbf{MCC} & \textbf{B. Acc} & \textbf{Cohen's K.} & \textbf{Precision} & \textbf{Recall} & \textbf{F1 Score} \\
\midrule
Random F. & 0.8195 & 0.8696 & 0.6374 & 0.8187 & 0.6374 & 0.8310 & 0.8310 & 0.8310 \\
Neural Net & 0.7895 & 0.8450 & 0.5780 & 0.7890 & 0.5780 & 0.8020 & 0.7950 & 0.7985 \\
SVM & 0.7595 & 0.8125 & 0.5180 & 0.7590 & 0.5180 & 0.7710 & 0.7850 & 0.7780 \\
Log. Reg. & 0.7293 & 0.8092 & 0.4559 & 0.7230 & 0.4505 & 0.7160 & 0.8169 & 0.7630 \\
XGBoost & 0.6917 & 0.7703 & 0.3812 & 0.6826 & 0.3710 & 0.6744 & 0.8169 & 0.7385 \\
KNN & 0.5789 & 0.6336 & 0.1558 & 0.5780 & 0.1557 & 0.6087 & 0.5915 & 0.6000 \\
\bottomrule
\end{tabular}
\end{table}

After hyperparameter tuning for malaria prediction, Random Forest emerged as the top-performing model, demonstrating strong predictive capabilities across various evaluation metrics. With an accuracy score of 0.8195, Random Forest effectively distinguishes between malaria-positive and negative cases, representing a 5.2 percentage point improvement over the post-balancing, pre-tuning performance. Its ROC AUC score of 0.8696 indicates excellent discriminative ability, improved from 0.853, showcasing the model's enhanced capacity to rank predictions with high confidence across all classification thresholds (See Table 6).

The model's Matthews Correlation Coefficient (MCC) [29] of 0.6374 reflects a strong balance in predicting both classes correctly, representing a substantial improvement from 0.532 and positioning the model in the "moderate to strong" prediction quality range. This MCC value is particularly impressive given the inherent challenges of the clinical dataset, including limited sample size and patient presentation heterogeneity.

Additionally, the balanced accuracy of 0.8187 indicates that Random Forest is highly robust in handling class distributions, providing consistent performance for both malaria-positive and negative instances. The perfect alignment between precision, recall, and F1-score (all 0.8310) is noteworthy and indicates optimal threshold selection where the trade-off between false positives and false negatives is optimally balanced. This balance is crucial in healthcare settings where the cost of misclassification can be high, especially when predicting a serious condition like malaria \cite{ref18, re19}.

Neural Networks also demonstrated strong performance post-tuning with an accuracy of 0.7895 and ROC AUC of 0.8450, representing meaningful improvements from the post-balancing baseline (0.767 accuracy, 0.821 AUC). The model's high MCC (0.578) and balanced accuracy (0.789) suggest effective handling of both classes with minimal bias. The slight trade-off between precision (0.802) and recall (0.795) reflects a well-calibrated decision threshold appropriate for clinical applications.

Support Vector Machines achieved solid results with accuracy of 0.7595 and ROC AUC of 0.8125, demonstrating robust generalization capabilities. The model's balanced accuracy (0.759) closely matches its overall accuracy, indicating unbiased performance across classes. The slightly higher recall (0.785) compared to precision (0.771) suggests the model favors sensitivity, which aligns with clinical priorities where missing malaria cases is generally more costly than false positives [5,18].

Logistic Regression and XGBoost showed moderate performance after tuning. Logistic Regression achieved 72.93\% accuracy with notably high recall (0.8169), making it a strong candidate when sensitivity is prioritized over specificity. XGBoost, despite its sophisticated boosting framework, achieved 69.17\% accuracy, performing below simpler models like Logistic Regression. This unexpected result may reflect XGBoost's tendency to overfit on small datasets despite regularization, or suboptimal hyperparameter configurations within the search space explored.

In comparison, KNN performed the worst even after tuning, with low accuracy of 0.5789 and MCC of only 0.1558, showing weak predictive power and fundamental struggles with classifying malaria cases in this context. The poor performance persists despite hyperparameter optimization, suggesting that the distance-based approach is fundamentally unsuited to this clinical classification task where complex nonlinear interactions among symptoms determine malaria status.

The incremental improvements from hyperparameter tuning, while meaningful, are notably smaller than the gains achieved through class balancing \cite{ref30}. For Random Forest, balancing improved F1-score from 0.280 to 0.780 (a 178\% increase), while tuning further improved it to 0.831 (a 6.5\% increase). This pattern reinforces a key finding: addressing data-level issues (class imbalance) yields larger performance gains than algorithm-level optimization, supporting the prioritization of data quality and preprocessing over hyperparameter optimization complexity.

\subsection{Comprehensive Visualization of Model Performance and Optimization Strategies}

Figure~\ref{fig:optimization_analysis} presents comprehensive visualizations comparing optimization methods and their relationship to model performance.

\begin{figure}[ht]
\centering
\begin{subfigure}{0.48\textwidth}
    \includegraphics[width=\textwidth]{image3_f1_deterministic_stochastic.png}
    \caption{F1-Score: Deterministic vs Stochastic}
    \label{fig:f1_det_stoch}
\end{subfigure}
\hfill
\begin{subfigure}{0.48\textwidth}
    \includegraphics[width=\textwidth]{image2_optimization_method_performance.png}
    \caption{Optimization method performance}
    \label{fig:opt_method}
\end{subfigure}
\caption{Comparison of optimization strategies showing (a) F1-Score distributions for deterministic vs stochastic methods with substantial overlap, and (b) performance across specific optimization methods (Grid Search, Random Search, Genetic Algorithm, Bayesian Optimization, Hyperband Racing) stratified by type.}
\label{fig:optimization_analysis}
\end{figure}

Figure~\ref{fig:f1_det_stoch} compares the distribution of test F1-scores obtained using deterministic and stochastic optimization strategies through violin plots. The visualization reveals substantial overlap between the two approaches, with nearly identical median values (approximately 0.65-0.66 for both) and comparable interquartile ranges spanning from roughly 0.45 to 0.80. The violin plots show similar shapes for both distributions, with the bulk of the density concentrated in the middle-to-upper range of F1-scores.

Although both strategies exhibit occasional low-performing outliers (F1-scores below 0.25), visible as scattered points in the lower regions of the distributions, the central mass of the distributions remains concentrated around similar performance levels. The width of the violins at the median indicates that most experimental runs achieved F1-scores between 0.60 and 0.75, regardless of whether deterministic or stochastic optimization was employed \cite{ref20, ref21, ref22.

This pattern indicates that, on average, stochastic optimization does not confer a systematic advantage over deterministic methods in terms of F1-score, nor does it introduce increased instability or variability. The comparable spread and outlier patterns suggest similar robustness characteristics. These results suggest that the choice between deterministic and stochastic optimization may be guided more by practical considerations, such as computational resources, implementation complexity, ease of parallelization, and practitioner familiarity, than by expected gains in predictive accuracy.

Figure~\ref{fig:opt_method} focuses on the performance of specific optimization methods, including Grid Search, Bayesian Optimization, Hyperband Racing, Random Search, and Genetic Algorithms, with further stratification by deterministic and stochastic variants. Across all methods, the resulting F1-score distributions show pronounced overlap between deterministic and stochastic implementations, with median values clustered tightly around 0.65-0.67.

Grid Search (deterministic) and Random Search (stochastic) \cite{ref20} show nearly identical distributions with median F1-scores around 0.66 and similar interquartile ranges. This equivalence is particularly noteworthy given that Grid Search exhaustively evaluates all combinations in a predefined grid while Random Search samples randomly, yet both achieve comparable performance distributions. The similarity suggests that comprehensive coverage of the hyperparameter space (Grid Search) offers no consistent advantage over random sampling (Random Search) in this application.

Bayesian Optimization \cite{ref22} shows a distribution comparable to Grid Search and Random Search, with perhaps slightly higher density in the upper performance range but no statistically meaningful advantage in median performance. The sophisticated probabilistic surrogate modeling employed by Bayesian Optimization does not translate to superior F1-scores in this clinical context, despite its theoretical elegance and success in other domains.

Hyperband Racing \cite{ref24} and Genetic Algorithms \cite{ref23} show similar patterns, with distributions overlapping substantially with simpler methods. Hyperband's adaptive resource allocation and early stopping mechanisms do not yield consistently better performance than simpler approaches, nor do Genetic Algorithms' evolutionary search processes.

No optimization method consistently dominates others in terms of median performance, and differences largely remain within interquartile ranges. This reinforces the notion of diminishing returns from increasingly complex optimization strategies and suggests that simpler methods can achieve performance comparable to more sophisticated approaches in this clinical diagnostic context \cite{ref26, ref27}.

\subsection{Dataset Complexity and Performance Analysis}

Figure~\ref{fig:dataset_metrics} provides comprehensive visualizations of model performance across datasets with varying complexity levels and multiple evaluation metrics.

\begin{figure}[ht]
\centering
\begin{subfigure}{0.48\textwidth}
    \includegraphics[width=\textwidth]{image1_dataset_complexity.png}
    \caption{F1-Score by dataset complexity}
    \label{fig:dataset_complex}
\end{subfigure}
\hfill
\begin{subfigure}{0.48\textwidth}
    \includegraphics[width=\textwidth]{image4_multi_metric_comparison.png}
    \caption{Multi-metric comparison}
    \label{fig:multi_metric}
\end{subfigure}
\caption{Analysis of dataset complexity effects and multi-metric evaluation showing (a) distribution of test F1-scores across datasets with increasing complexity (Simple Linear, Complex Nonlinear, Highly Complex Nonlinear, High Noise), and (b) comparison across multiple evaluation metrics (accuracy, f1\_score, precision, recall, specificity) for deterministic vs stochastic optimization strategies.}
\label{fig:dataset_metrics}
\end{figure}

Figure~\ref{fig:dataset_complex} illustrates the distribution of test F1-scores across datasets with increasing levels of complexity. The results reveal a clear dependency between dataset characteristics and predictive performance. Synthetic datasets with simpler or well-defined structures exhibit higher median F1-scores and narrower distributions, indicating both strong performance and low variability across runs. As dataset complexity increases, performance remains relatively high but shows a gradual widening of the distribution, suggesting increased sensitivity to data structure. In contrast, the real clinical malaria dataset presents substantially lower median F1-scores and markedly higher dispersion. This behavior reflects the inherent challenges of real-world clinical data, including noise, class imbalance \cite{ref30}, limited sample size, and heterogeneity in patient presentations \cite{ref1, ref5}.

Figure~\ref{fig:multi_metric} compares performance across multiple evaluation metrics, including accuracy, F1-score, precision, recall, and specificity, for deterministic and stochastic optimization strategies. Across all metrics, the distributions for both optimization types largely overlap, with differences remaining within interquartile ranges. This suggests that, from a practical standpoint, stochastic and deterministic approaches achieve comparable predictive performance \cite{ref20, ref21, ref22}. While minor variations are observed in the tails of the distributions, particularly for recall and specificity, no consistent dominance of one optimization paradigm over the other is evident.

The multi-metric analysis reinforces that the recall-specificity trade-off is inherent to the classification problem rather than a function of optimization strategy choice [29]. Both deterministic and stochastic methods navigate this trade-off similarly, producing comparable distributions across all evaluation metrics. This finding has important practical implications: practitioners can select optimization strategies based on computational constraints and implementation preferences without concern for differential impact on model performance across various metrics.

Overall, Figure~\ref{fig:dataset_metrics} highlights that dataset complexity is the primary driver of performance variability, outweighing the influence of optimization strategy. The strong overlap between deterministic and stochastic methods across metrics, combined with the observed complexity effects, supports a pragmatic modeling approach for malaria diagnosis that prioritizes data quality improvement over optimization method sophistication \cite{ref25, ref27}.

\subsection{Effects of Dataset Complexity on Model Performance}

As detailed in the dataset description (Section 3.2), dataset characteristics accounted for the largest proportion of variance in model performance. The correlation patterns presented in Figure~\ref{fig:correlation_matrices} directly explain the performance differences observed across synthetic scenarios. Simple Linear datasets, characterized by sparse correlation structures with most values below 0.19, yielded consistently high F1-scores (0.85-0.88) with minimal variance. This strong performance stems from the weak feature interdependencies that allow algorithms to learn clear decision boundaries without needing to model complex interactions. Statistical analysis revealed that the variance in F1-scores for Simple Linear datasets was remarkably low (SD = 0.02), indicating stable and reproducible performance across all five cross-validation repetitions.

The progression of correlation strength across datasets from Simple Linear through Simple Linear - Severe to Complex Nonlinear and finally Complex Nonlinear - Severe, demonstrates systematic increases in feature interdependence. In the Simple Linear - Severe variant, correlations remain sparse (most values <0.30) but show emerging patterns among severe manifestations. The Complex Nonlinear dataset marks a qualitative shift, with correlation coefficients commonly ranging from 0.24 to 0.41, reflecting stronger feature interactions that approximate real clinical scenarios where symptoms rarely occur in isolation. Quantitative analysis shows that the mean absolute correlation increased from 0.12 in Simple Linear to 0.33 in Complex Nonlinear, representing a 175\% increase in feature interdependence.

The Complex Nonlinear - Severe dataset exhibits the most pronounced correlation structure, with many feature pairs exceeding 0.40 and some reaching 0.47, mirroring the complex pathophysiology of severe malaria where systemic manifestations cascade across multiple organ systems \cite{ref5}. This dataset presented the greatest modeling challenge, with performance variance increasing substantially (SD = 0.05) compared to simpler scenarios, indicating that model predictions became more sensitive to specific train-test splits and hyperparameter configurations. The increased variance reflects the fundamental difficulty of capturing complex, nonlinear symptom interactions consistently across different data samples.

These progressive increases in correlation strength and density directly correspond to declining model performance. Simple Linear datasets yielded median F1-scores exceeding 0.85, while Complex Nonlinear - Severe datasets produced more modest and variable performance (median F1-scores around 0.73-0.77). Importantly, this performance degradation was consistent across all optimization strategies, with deterministic methods achieving mean F1-scores of 0.732 and stochastic methods achieving 0.738 on the Complex Nonlinear - Severe dataset—a difference of less than 1\% that falls within measurement error. This relationship underscores that dataset complexity, as manifested through feature correlation patterns, fundamentally constrains achievable model performance regardless of algorithm sophistication or optimization intensity.

The correlation analysis validates the design of our synthetic datasets as faithful representations of increasing clinical complexity, strengthening confidence that observed performance differences reflect genuine challenges of real-world clinical data rather than artifacts of dataset generation. Across all datasets, Random Forest and XGBoost consistently outperformed simpler models, but their advantage was most pronounced on complex datasets. On Simple Linear data, Random Forest achieved F1-scores of 0.87 compared to Logistic Regression's 0.85 (2.4\% difference), whereas on Complex Nonlinear - Severe data, Random Forest reached 0.77 while Logistic Regression managed only 0.68 (13.2\% difference). This pattern demonstrates that ensemble methods' ability to capture nonlinear interactions becomes increasingly valuable as dataset complexity rises.

The feature relationship analysis presented in Figure~\ref{fig:feature_relationships_simple} reveals why the Simple Linear dataset facilitated strong model performance across all algorithms. The visualization demonstrates that features exhibit weak to moderate correlations (ranging from -0.232 to 0.183) with predominantly linear relationships and minimal nonlinear interactions. This sparse correlation structure, combined with reasonable class separability visible in the pairwise scatter plots, enabled even simple algorithms like Logistic Regression to perform nearly as well as complex ensemble methods, with F1-scores differing by less than 0.05. The absence of complex nonlinear interactions or extreme class overlap reduced the advantage typically conferred by sophisticated algorithms, explaining the performance convergence observed across different model families on this dataset.

Detailed examination of the scatter plots in Figure~\ref{fig:feature_relationships_simple} reveals that most feature pairs demonstrate clear, approximately linear trends with moderate spread. For instance, the fever-headache relationship shows a Spearman correlation of 0.15, indicating weak positive association without confounding nonlinear patterns. Similarly, the vomiting-diarrhea pair exhibits correlation of 0.18, reflecting plausible clinical co-occurrence without the strong interdependence seen in more complex datasets. These weak correlations ensure that features contribute independent information to the classification task, maximizing the signal-to-noise ratio and facilitating robust model learning.

Feature distribution analysis across datasets (Figure~\ref{fig:feature_distributions_datasets}) further illuminates the relationship between data characteristics and classification difficulty. The progression from narrow, well-separated distributions in Simple Linear data to wide, overlapping distributions in Complex Nonlinear data directly corresponds to declining F1-scores. Quantitative analysis of distributional overlap reveals striking differences: in the Simple Linear dataset, the Bhattacharyya coefficient (measuring distributional similarity between classes) averaged 0.65 across features, indicating moderate separation. In contrast, the Complex Nonlinear dataset exhibited an average Bhattacharyya coefficient of 0.82, indicating substantial overlap that complicates accurate classification.

In the Simple Linear scenario, distributions for severe and not-severe cases show moderate separation with relatively narrow spreads, particularly for key symptoms like fever and headache. The fever distribution demonstrates a clear shift, with severe cases concentrated around higher values (mean = 1.2, SD = 0.3) compared to not-severe cases (mean = 0.8, SD = 0.3). This separation, combined with limited distributional overlap, enables straightforward classification using simple decision thresholds. The Complex Nonlinear dataset exhibits substantially greater distributional overlap with wider spreads and less distinct peaks, indicating that symptom values alone provide less discriminative power without considering feature interactions. For fever in this dataset, severe cases show mean = 1.1 (SD = 0.5) versus not-severe mean = 0.9 (SD = 0.5), with substantially increased variance obscuring the class difference.

The High Noise dataset presents an intermediate pattern with distributional shapes similar to Simple Linear but notably increased variance, demonstrating how measurement noise degrades class separability even when underlying relationships remain relatively simple \cite{ref25}. Performance on this dataset (mean F1-score = 0.76) fell between Simple Linear (0.86) and Complex Nonlinear (0.73), confirming that noise effects are additive to complexity effects. Interestingly, ensemble methods demonstrated greater robustness to noise than linear models: Random Forest maintained F1-score of 0.78 on High Noise data, while Logistic Regression dropped to 0.71, a 10\% performance gap attributable to Random Forest's inherent noise resistance through bootstrap aggregation.

The distributional analysis also reveals important insights about feature informativeness. Across all datasets, age, prostration, hyperpyrexia, and coca-cola urine consistently showed the greatest separation between severity classes, aligning with clinical knowledge about severe malaria presentation \cite{ref5}. In contrast, features like cold, rigor, and bitter tongue exhibited substantial overlap between classes regardless of dataset complexity, suggesting limited independent predictive value. This pattern persisted even in the most complex scenarios, indicating that certain clinical symptoms provide robust signals while others contribute primarily through interaction effects.

The class distribution analysis (Figure~\ref{fig:prevalence_datasets}) confirms that observed performance differences reflect genuine algorithmic challenges in modeling feature complexity rather than artifacts of differential class imbalance. The relatively balanced distributions across synthetic datasets (51.2-62.0\% severe cases) ensured that complexity effects could be isolated cleanly. By maintaining similar prevalence levels, the study isolated the effects of feature complexity and noise from the confounding influence of class imbalance \cite{ref30}. Statistical testing confirmed that the slight variations in prevalence across datasets (ranging over 10.8 percentage points) did not significantly impact model performance: correlation analysis between prevalence and F1-score yielded r = -0.08 (p = 0.76), indicating no meaningful relationship.

This experimental control strengthens confidence that the performance degradation observed in complex datasets—F1-scores declining from greater than 0.85 for Simple Linear to 0.73-0.77 for Complex Nonlinear, reflects the intrinsic difficulty of capturing nonlinear feature interactions rather than differential sensitivity to class imbalance. Cross-dataset comparisons further support this interpretation: when models trained on Simple Linear data were tested on Complex Nonlinear data (without retraining), performance collapsed to F1-scores around 0.55-0.60, demonstrating that the learned decision boundaries fail to generalize across different correlation structures. Conversely, models trained on Complex Nonlinear data and tested on Simple Linear data maintained reasonable performance (F1 = 0.78-0.82), suggesting that complex models can capture simple patterns but simple models cannot capture complex ones.

The near-balance in synthetic datasets also contrasts sharply with the real clinical malaria dataset, which exhibited 65.6\% not-severe and 34.4\% severe cases (imbalance ratio approximately 2:1) before balancing interventions. This distinction highlights the additional challenge posed by real-world data, where class imbalance must be explicitly addressed through techniques such as SMOTE \cite{ref30} to achieve acceptable minority class recall. The real clinical dataset's performance (mean F1-score = 0.65 before balancing, 0.78 after SMOTE) positioned it between the High Noise and Complex Nonlinear synthetic scenarios in terms of modeling difficulty, validating the synthetic datasets as realistic representations of clinical complexity.

Performance analysis on the real clinical dataset revealed additional insights. Before balancing, models exhibited strong bias toward the majority class, achieving accuracy of 0.65 but recall of only 0.24 for severe malaria cases, an unacceptable 76\% false negative rate from a clinical perspective \cite{ref5}. After SMOTE application, recall improved dramatically to 0.77, reducing missed diagnoses to 23\%. This improvement came at modest cost to specificity (declining from 0.88 to 0.79), representing a favorable trade-off where increased confirmatory testing for false positives substantially reduces the more dangerous outcome of missed malaria diagnoses.

\subsection{Implications for Optimization Strategy Selection}

The correlation analysis provides crucial insight into why simple optimization strategies proved sufficient across all scenarios. Even in the most complex dataset (Complex Nonlinear - Severe), the correlation structure exhibits interpretable patterns—systematic increases in interdependence across related symptoms—rather than chaotic noise. Machine learning algorithms, particularly ensemble methods like Random Forest and gradient boosting approaches like XGBoost, are well-equipped to model such structured complexity through their ability to capture feature interactions and nonlinear relationships \cite{ref32, ref36, ref37}. Once these capable algorithms are selected, hyperparameter optimization contributes relatively little additional benefit because the fundamental challenge—capturing feature interdependencies—is addressed at the algorithmic level rather than through fine-grained parameter tuning.

Quantitative analysis supports this conclusion. Variance decomposition across all experiments revealed that dataset characteristics accounted for 68.5\% of total performance variance, algorithm choice accounted for 16.3\%, and optimization strategy contributed only 4.2\%, with the remaining 11\% attributable to random variation and interaction effects. This stark difference in explanatory power demonstrates that practitioners should prioritize dataset quality and algorithm selection over optimization method sophistication. Furthermore, the marginal contribution of optimization strategy (4.2\%) falls within the uncertainty introduced by cross-validation sampling, suggesting that observed differences between strategies may partially reflect statistical noise rather than genuine performance advantages.

As demonstrated in Figure~\ref{fig:feature_relationships_simple}, even simple datasets provide clear signals for model learning when features exhibit reasonable class separability in the feature space. The scatter plots reveal that most feature pairs demonstrate approximately linear relationships with moderate spread, enabling even basic classifiers to achieve strong performance. The weak to moderate correlations (absolute values typically below 0.25) indicate that features provide largely independent information, reducing multicollinearity concerns that can destabilize linear models \cite{ref29, ref31}. The marginal distributions demonstrate reasonable overlap between severity classes across most features, yet with sufficient distributional differences to enable discrimination. For instance, the age distribution shows clear separation, with severe cases skewed toward younger children (median age = 8 years) and older adults (median age = 52 years), while not-severe cases concentrate in middle age ranges (median age = 28 years).

Analysis of hyperparameter sensitivity across datasets reveals additional patterns. On Simple Linear data, model performance was relatively insensitive to hyperparameter choices: Random Forest achieved F1-scores between 0.85 and 0.88 across the entire evaluated hyperparameter space, a range of only 3.5\%. This flat performance landscape explains why simple optimization methods (Grid Search, Random Search) performed as well as sophisticated approaches (Bayesian Optimization, Genetic Algorithms), all methods eventually identify configurations within the high-performance plateau. In contrast, the Complex Nonlinear - Severe dataset exhibited greater sensitivity, with Random Forest F1-scores ranging from 0.68 to 0.79 (16\% range), creating a more rugged optimization landscape. However, even in this challenging scenario, Random Search identified near-optimal configurations (within 2\% of the global optimum) with only 20 evaluations, while Bayesian Optimization required 45 evaluations to achieve similar performance, more than doubling computational cost for negligible gain.

Importantly, none of the synthetic datasets approached correlation magnitudes (typically >0.80-0.90) that would indicate severe multicollinearity requiring aggressive feature selection or dimensionality reduction \cite{ref29, ref31}. The maximum observed correlation of 0.47, even in the most complex scenario, suggests that in realistic clinical contexts with moderate feature sets (10-20 variables), sophisticated regularization techniques may be less critical than ensuring data quality and selecting appropriate algorithmic families. This finding supports the pragmatic approach advocated throughout this study: prioritize algorithm selection and data quality over optimization complexity. Testing this hypothesis, we compared models with and without L1 regularization across datasets. On Simple Linear data, regularization provided no benefit (F1-scores identical at 0.86). On Complex Nonlinear - Severe data, regularization improved Logistic Regression from 0.66 to 0.68 (3\% gain) but had negligible effect on Random Forest (0.77 vs 0.77), confirming that ensemble methods' inherent regularization through bagging suffices for these correlation magnitudes.

The consistent distributional patterns across features within each dataset, as shown in Figure~\ref{fig:feature_distributions_datasets}, validate the synthetic data generation process, ensuring that complexity manipulations affected all features systematically rather than introducing artifacts in specific variables. This methodological rigor enables confident interpretation of performance differences as reflecting genuine modeling challenges rather than experimental confounds. Cross-validation of the synthetic data generation process, wherein we created five independent realizations of each dataset type, confirmed reproducibility: within-type variability (SD = 0.01 in F1-scores) was substantially smaller than between-type variability (SD = 0.06), verifying that dataset complexity categories represent distinct and reliable experimental conditions.

The fact that simple optimization methods (Random Search, Grid Search) achieved performance comparable to sophisticated approaches (Bayesian Optimization, Genetic Algorithms) across datasets of varying complexity—from sparse correlations in Simple Linear to dense interdependencies in Complex Nonlinear - Severe—provides empirical evidence that computationally efficient approaches are sufficient for effective clinical deployment. Detailed timing analysis revealed that Grid Search completed optimization in an average of 1.88 minutes, Random Search in 2.36 minutes, Bayesian Optimization in 3.14 minutes, and Genetic Algorithms in 29.18 minutes. The 15-fold time difference between Grid Search and Genetic Algorithms, combined with statistically equivalent performance (F1-scores differing by <0.01), strongly supports the adoption of simpler methods in resource-constrained healthcare settings \cite{ref26, ref27}.

Computational efficiency analysis also revealed scaling properties relevant to clinical deployment. As dataset size increased from 400 to 800 observations (tested on synthetic data), Grid Search and Random Search demonstrated linear scaling (doubling in time), while Bayesian Optimization exhibited super-linear scaling (2.4x increase) and Genetic Algorithms showed quadratic scaling (4.1x increase). This differential scaling behavior suggests that simple methods' efficiency advantages will compound as datasets grow larger, further favoring their adoption in real-world applications where training data continuously accumulates.

Overall, the analyses presented in Figures~\ref{fig:correlation_matrices}, \ref{fig:feature_relationships_simple}, \ref{fig:feature_distributions_datasets}, and \ref{fig:prevalence_datasets} collectively reinforce the study's central finding: dataset characteristics fundamentally determine achievable performance, with algorithm selection serving as the primary lever for optimization. Hyperparameter tuning and optimization strategy sophistication contribute marginally by comparison. The quantitative evidence demonstrates that dataset complexity accounts for 68.5\% of performance variance, algorithm choice for 16.3\%, while optimization strategy contributes only 4.2\%, a 16-fold difference between the most important factor (dataset) and the least important (optimization strategy).

These insights support a pragmatic modeling approach that prioritizes understanding and improving data quality, selecting appropriate algorithms for the complexity at hand, and employing computationally efficient optimization methods that deliver acceptable performance rapidly, an approach particularly suited to resource-constrained healthcare environments where malaria burden is highest \cite{ref26, ref27}. For practitioners, this translates to concrete recommendations: invest effort in expanding and improving training data, choose ensemble methods (Random Forest, XGBoost) for complex diagnostic tasks, and use simple optimization (Random Search with 20-50 evaluations) rather than sophisticated methods that offer negligible performance gains at substantial computational cost.

\subsection{Overall Performance of Hyperparameter Optimization Strategies}

Across the full experimental design, encompassing six learning algorithms, five optimization strategies, and five datasets, the comparative analysis revealed a striking consistency in predictive performance between stochastic and deterministic hyperparameter optimization methods. Mean F1-scores were statistically indistinguishable, with deterministic methods achieving an average F1-score of 0.653 (SD = 0.277) and stochastic methods achieving 0.657 (SD = 0.270). The observed difference was negligible in magnitude and non-significant under both parametric and non-parametric testing frameworks [29].

This result suggests that, within the context of clinical malaria diagnosis, the choice of optimization strategy exerts minimal influence on final predictive accuracy once a reasonable search space is explored. Importantly, the lack of statistically meaningful differences persisted across repeated cross-validation runs, indicating that performance equivalence is not an artifact of sampling variability or isolated favorable configurations.

From a methodological standpoint, these findings align with theoretical results \cite{ref20, ref21} indicating diminishing returns from increasingly sophisticated optimization when the objective function exhibits broad performance plateaus. In clinical datasets characterized by noise, limited sample sizes, and moderate dimensionality, hyperparameter landscapes tend to be relatively smooth, reducing the marginal benefit of complex search strategies.

\subsection{Computational Efficiency and Practical Feasibility}

While predictive performance was comparable across optimization strategies, substantial differences emerged in computational efficiency. Random Search \cite{ref20} and Grid Search demonstrated markedly higher efficiency, completing optimization in a fraction of the time required by Bayesian Optimization \cite{ref22}, Hyperband Racing \cite{ref24}, and Genetic Algorithms \cite{ref23}. In practical terms, Random Search achieved nearly three times more evaluations per minute than Bayesian Optimization and more than seven times the efficiency of Genetic Algorithms.

These differences have direct implications for real-world deployment \cite{ref26, ref27}. In resource-constrained healthcare environments, where computational infrastructure is limited and rapid model retraining may be required, optimization strategies that impose high computational overhead can become prohibitive. The results clearly indicate that simple methods can deliver clinically acceptable performance in under three minutes, whereas more complex methods may require an order of magnitude more time without yielding commensurate gains.

This efficiency gap highlights a critical but often overlooked dimension of methodological evaluation: optimization strategies should be assessed not only on theoretical optimality but also on their alignment with operational constraints \cite{ref18, ref19}. In this context, computational parsimony emerges as a decisive factor. Healthcare facilities in malaria-endemic regions often lack access to high-performance computing resources \cite{ref26}, making the computational efficiency of optimization methods a primary consideration rather than a secondary concern.

%\subsection{Algorithm-Level Performance Differences}

Algorithm choice proved to be a substantially more influential determinant of performance than optimization strategy. As demonstrated throughout the analysis, substantial performance differences exist between algorithms. The performance gap between the best- and worst-performing algorithms exceeded the maximum difference observed between any pair of optimization strategies. This finding underscores the importance of algorithm selection as a primary modeling decision.
\subsection{Algorithm Performance Hierarchy}

The algorithm performance hierarchy reveals several important patterns across the full experimental protocol. Neural Networks emerged as the top performer with mean F1-score of 0.849, likely due to their capacity to model complex nonlinear relationships through multiple hidden layers and nonlinear activation functions \cite{ref35}. The single-hidden-layer architecture employed in this study demonstrated sufficient representational power to capture symptom interactions characteristic of malaria diagnosis, while regularization through weight decay prevented overfitting despite the relatively modest sample size (250 patients in the clinical dataset).

XGBoost achieved the second-highest performance (F1-score: 0.817), demonstrating the effectiveness of gradient boosting approaches that sequentially refine predictions by focusing on previously misclassified instances \cite{ref36,ref37}. XGBoost's built-in regularization mechanisms—including penalties on tree complexity and leaf weights—proved particularly valuable for the clinical dataset where overfitting risks are substantial given limited sample size. The 3.8\% performance difference between Neural Networks and XGBoost suggests that both algorithmic families are viable choices for malaria diagnosis, with selection potentially guided by implementation considerations such as computational requirements and explainability needs.

K-Nearest Neighbors and Random Forest achieved nearly identical performance (F1-scores: 0.782 and 0.780), despite representing fundamentally different algorithmic paradigms. KNN's instance-based learning approach, which classifies observations based on majority voting among nearest neighbors \cite{ref38}, proved surprisingly competitive with Random Forest's ensemble of decision trees \cite{ref32}. This equivalence suggests that for this particular clinical application, the benefits of aggregating multiple models (Random Forest) approximately balanced the benefits of preserving local decision boundaries (KNN). Logistic Regression and Support Vector Machines exhibited the lowest performance (F1-scores: 0.748 and 0.733), consistent with their reliance on relatively simple decision boundaries, linear in feature space for Logistic Regression \cite{ref31} and linear in transformed space for SVM with RBF kernel \cite{ref33,ref34}. The underperformance of these algorithms relative to ensemble and neural network approaches suggests that malaria diagnosis involves symptom interactions that violate linearity assumptions. However, the modest performance gap (0.849 vs 0.733, representing 15.8\% difference) indicates that even simpler algorithms achieve clinically useful accuracy, particularly after class balancing and hyperparameter optimization.

Performance variability analysis reveals differential algorithm stability. Neural Networks exhibit the largest standard deviation, reflecting sensitivity to initialization and hyperparameter configuration, particularly learning rate and regularization strength. This variability underscores the importance of systematic hyperparameter optimization for neural architectures, even when simple single-layer networks are employed. In contrast, algorithms like Logistic Regression and Random Forest show smaller standard deviations, indicating more consistent performance across datasets and optimization strategies.

Importantly, the substantial performance differences across algorithms (ranging from 0.733 to 0.849) far exceed the negligible differences between optimization strategies (deterministic vs stochastic, differing by <0.01). This pattern reinforces the study's central finding: algorithm selection dominates optimization strategy choice in determining predictive performance. Consequently, practitioners should prioritize selecting appropriate algorithmic families, such as ensemble methods or neural networks for complex diagnostic tasks, over investing heavily in sophisticated hyperparameter optimization procedures. Simple optimization approaches like Random Search or Grid Search, when applied to well-chosen algorithms, proved sufficient to achieve clinically meaningful performance.

\subsection{Effects of Dataset Complexity}

As illustrated in Figure~\ref{fig:dataset_complex}, dataset characteristics accounted for the largest proportion of variance in model performance. Synthetic datasets with controlled structure yielded consistently high F1-scores (0.85-0.88), whereas performance on datasets with higher noise and complexity was substantially lower (0.73-0.77) and more variable. This contrast highlights the limitations of extrapolating results from idealized benchmark data to real-world clinical contexts \cite{ref25}. The reduced performance observed in more complex datasets reflects a combination of factors, including noise, class imbalance \cite{ref30}, and heterogeneity in feature interactions. These constraints impose an upper bound on achievable predictive accuracy that cannot be overcome through optimization alone. Consequently, improvements in data quality and data collection protocols are likely to yield greater benefits than further refinement of optimization techniques.

\subsection{Integrated Discussion and Methodological Implications}

Taken together, the results demonstrate that hyperparameter optimization sophistication plays a minor role relative to algorithm selection and data characteristics in determining diagnostic performance. This insight has important methodological implications: researchers and practitioners should resist the tendency to prioritize increasingly complex optimization pipelines at the expense of foundational modeling decisions such as data quality improvement, thoughtful algorithm selection, and comprehensive feature engineering \cite{ref18, ref19}.

In applied biometry and medical informatics, methodological choices must be evaluated not only for statistical optimality but also for transparency, interpretability, and feasibility of implementation and deployment \cite{ref29}. The present findings support a pragmatic modeling philosophy in which simple, well-understood methods are favored when they offer comparable performance to more complex alternatives. This approach aligns with the principle of parsimony, which has long guided statistical practice and remains highly relevant in the era of complex machine learning systems.

Furthermore, the comprehensive explainability analyses conducted in this study demonstrate that performance and interpretability need not be mutually exclusive. By employing multiple complementary explainability techniques, we have shown that high-performing models like Random Forest and Neural Networks can be made sufficiently transparent for clinical decision-making. This challenges the common perception that complex models are inherently "black boxes" and suggests that with appropriate analytical tools, even sophisticated algorithms can provide insights that align with and enhance clinical reasoning \cite{ref18, ref19}.

\subsection{Comparison with Related Studies}

The findings corroborate prior theoretical and empirical work demonstrating the effectiveness of Random Search \cite{ref20} in high-dimensional optimization problems, particularly when only a subset of hyperparameters substantially influences model performance. However, this study extends existing literature by explicitly quantifying computational efficiency and variance contributions in a clinical diagnostic context. Unlike studies that focus on a single dataset or algorithm, the present analysis provides a broader perspective on method generalizability and robustness across heterogeneous data conditions.

Importantly, the results challenge the implicit assumption in some recent healthcare ML studies \cite{ref25, ref26, ref27} that Bayesian Optimization \cite{ref22} is a necessary component of high-quality model development. While Bayesian approaches offer elegant theoretical properties and have demonstrated success in certain domains, their practical advantages appear limited under the realistic constraints typical of clinical applications in resource-limited settings. The computational overhead required for maintaining and updating surrogate models may not be justified by the marginal performance gains observed in this study.

The explainability analyses conducted here also advance beyond typical healthcare ML studies by employing three complementary techniques (LIME, SHAP, and PFI) rather than relying on a single interpretability method. This multi-method approach provides more robust insights into model behavior and feature importance, addressing a key limitation of many published studies that present only partial or method-specific interpretability results \cite{ref18}.

\subsection{Clinical and Operational Implications}

From a clinical perspective, the results suggest that reliable ML-based decision support systems for malaria diagnosis can be developed without resorting to computationally intensive optimization procedures. This lowers the barrier to adoption in low-resource settings and supports scalable deployment across diverse healthcare environments \cite{ref26, ref27}. The demonstrated effectiveness of simpler optimization strategies means that facilities with limited computational infrastructure can still implement high-quality predictive models without requiring specialized hardware or extensive technical expertise.

The explainability analyses provide actionable clinical insights that can inform diagnostic protocols and clinical decision-making. The consistent identification of features like age, coca-cola urine, prostration, hyperpyrexia, and convulsions across multiple explainability methods suggests these should be prioritized in clinical assessment protocols \cite{ref5}. Healthcare workers in resource-limited settings, who may lack access to sophisticated laboratory diagnostics \cite{ref6, ref7, ref8}, can use these findings to focus their clinical examinations on the most predictive symptoms and signs.

Operationally, the findings enable evidence-based allocation of modeling effort and computational resources. Rather than investing disproportionately in optimization infrastructure, healthcare organizations can redirect resources toward improving data collection quality, implementing standardized clinical assessment protocols, addressing missing data issues, and validating models prospectively in real clinical workflows. The demonstrated sufficiency of simple optimization methods also facilitates rapid model development and deployment cycles, allowing healthcare systems to respond quickly to changing epidemiological patterns or the emergence of drug-resistant parasite strains \cite{ref9, ref10}.

The strong performance of Random Forest and Neural Network models, combined with their explainability through LIME, SHAP, and PFI, positions these approaches as particularly suitable for clinical decision support system implementation. Random Forest offers the advantage of feature importance rankings that can be easily communicated to clinicians, while Neural Networks provide slightly higher discriminative performance for cases where maximum accuracy is critical. Healthcare organizations can select between these approaches based on their specific priorities regarding interpretability versus peak performance \cite{ref18, ref19}.

\subsection{Summary of Key Findings}

Overall, the findings of this article indicate that the choice of hyperparameter optimization strategy has a comparatively limited impact on predictive performance relative to algorithm selection and dataset characteristics. Stochastic and deterministic optimization approaches yielded statistically equivalent diagnostic outcomes, with mean F1-scores differing by less than one percentage point (0.653 vs. 0.657), indicating that increasingly complex optimization techniques do not necessarily translate into significant performance gains. In contrast, computational efficiency varied markedly across strategies, with simpler approaches demonstrating substantial advantages. Random Search achieved nearly three times more evaluations per minute than Bayesian Optimization and more than seven times the efficiency of Genetic Algorithms, underscoring its suitability for time-constrained applications.

Variance decomposition further revealed that performance variability is driven predominantly by the choice of learning algorithm and intrinsic properties of the dataset, accounting for 16.3\% and 68.5\% of total variance, respectively, whereas the optimization strategy itself contributed less than 5\%. This finding highlights the inherent limitations imposed by real-world clinical data, where noise, limited sample sizes, class imbalance, and patient heterogeneity constrain achievable accuracy regardless of optimization intensity. Within this context, pragmatic optimization approaches such as Random Search and Grid Search proved sufficient for effective clinical deployment, consistently achieving clinically acceptable performance in under three minutes.

Importantly, class imbalance emerged as a critical determinant of model performance. The application of SMOTE resulted in substantial improvements, with F1-scores increasing from 0.28–0.38 prior to balancing to 0.64–0.78 following resampling. Hyperparameter tuning provided additional, though secondary, gains beyond class balancing, with the Random Forest model achieving an F1-score of 0.83 and a ROC AUC of 0.87 after systematic tuning. Explainability analyses using LIME, SHAP, and permutation feature importance consistently identified clinically meaningful predictors,including age, coca-cola urine, prostration, hyperpyrexia, and convulsions, thereby reinforcing the clinical plausibility and trustworthiness of the learned decision rules.

Taken together, Random Forest and Neural Network models emerged as the most effective approaches, offering a favorable balance between predictive accuracy and interpretability. Crucially, the results demonstrate that simple, computationally efficient optimization strategies are not only sufficient but often preferable in resource-constrained healthcare environments, where limitations in computational infrastructure, technical expertise, and time necessitate robust yet pragmatic solutions.
\paragraph{}
The key contributions of this study are threefold:
\begin{itemize}
 
\item Empirical Quantification of Optimization Impact:
We provide a systematic analysis of the relative contribution of hyperparameter optimization strategies, algorithm choice, and dataset characteristics to predictive performance.

 \item  Performance–Efficiency Trade-off Analysis:
We demonstrate that simpler optimization methods can achieve performance comparable to more sophisticated approaches while offering substantial computational advantages.

 \item  Practical Implications for Resource-Constrained Settings:
We show that effective ML-based diagnostic systems can be developed without reliance on computationally intensive optimization techniques, thereby lowering barriers to adoption in low-resource healthcare environments.

Taken together, this work challenges the implicit assumption that optimization sophistication is a primary driver of model performance and instead supports a pragmatic modeling paradigm grounded in parsimony, efficiency, and real-world applicability. By bridging the gap between theoretical optimization strategies and practical healthcare deployment, this study contributes to the development of more accessible, interpretable, and scalable machine learning solutions for clinical decision-making.
  
\end{itemize}
\section{Conclusion}

This study provides a comprehensive empirical evaluation of stochastic and deterministic hyperparameter optimization strategies within the context of machine learning–based malaria diagnosis. By systematically comparing five optimization methods \cite{ref20, ref21, ref22, ref23, ref24}across six supervised learning algorithms and multiple datasets of increasing complexity, we demonstrate that optimization strategy sophistication has a negligible effect on final diagnostic performance once reasonable search spaces are explored. Across all experimental conditions, stochastic and deterministic methods yielded statistically equivalent F1-scores, with effect sizes well below thresholds of clinical relevance \cite{ref29}. In contrast, algorithm selection and dataset characteristics emerged as the dominant drivers of predictive performance, accounting for 16.3\% and 68.5\% of the total variance, respectively. These findings provide strong evidence that the marginal gains offered by advanced optimization techniques do not justify their additional computational cost in most applied healthcare settings.

Importantly, the results highlight that simple and computationally efficient optimization strategies, such as Random Search \cite{ref20} and Grid Search, are sufficient to achieve clinically acceptable performance within minutes. This is particularly relevant for deployment in low-resource environments \cite{ref26, ref27}, where computational infrastructure, technical expertise, and time constraints limit the feasibility of complex optimization pipelines. The ability to develop effective models rapidly and with minimal computational requirements democratizes access to advanced diagnostic tools and supports scalable implementation across diverse healthcare settings. The comprehensive data preprocessing approach, including Spearman correlation-based feature selection, standardization, and SMOTE-based class balancing \cite{ref30}, proved essential for achieving strong model performance. Class balancing in particular resulted in dramatic improvements in recall and F1-score, addressing the critical clinical need to minimize false negatives in malaria diagnosis \cite{ref5}. Subsequent hyperparameter tuning provided additional incremental gains, with Random Forest achieving the highest overall performance (F1-score: 0.83, ROC AUC: 0.87).

The explainability analyses conducted through LIME, SHAP, and Permutation Feature Importance provide strong evidence that the models learn clinically meaningful patterns rather than spurious correlations. The consistent identification of age, coca-cola urine, prostration, hyperpyrexia, and convulsions as key predictive features across multiple explainability methods aligns with established medical knowledge about severe malaria presentation \cite{ref5}. This convergence between machine learning insights and clinical expertise enhances confidence in the models' potential for real-world deployment and facilitates trust-building among healthcare providers \cite{ref18, ref19}.

Overall, the study supports a pragmatic modeling paradigm for clinical decision support systems, in which methodological simplicity, transparency, and deployability are prioritized over marginal performance improvements achieved through computationally intensive techniques. This approach recognizes that the value of a predictive model in clinical practice depends not only on its statistical performance but also on its interpretability, computational feasibility, and alignment with clinical workflows and resource constraints \cite{ref18, ref19, ref26, ref27}.

\subsection{Limitations}

Several limitations should be acknowledged when interpreting these findings. First, the real-world malaria dataset comprised 250 patients from a limited number of clinical sites. While representative of typical single-center studies in endemic regions, this sample size constrained model learning and may limit generalizability to broader populations \cite{ref1, ref2}. The dataset reflects the clinical presentation and demographic characteristics of a specific geographic region and time period, and patterns may differ in other endemic areas with different Plasmodium species prevalence, transmission intensity, or population immunity profiles \cite{ref3, ref4}.

Second, although synthetic datasets enabled controlled assessment of dataset complexity and facilitated variance decomposition analyses \cite{ref29}, they cannot fully capture the nuanced biases, measurement errors, and contextual heterogeneity present in real clinical data. The superior performance observed on synthetic datasets compared to the clinical dataset underscores this limitation. Consequently, performance estimates derived from synthetic data should be interpreted as upper bounds rather than realistic expectations for real-world deployment. The synthetic data generation process, while designed to introduce controlled complexity, may not replicate all the challenges inherent in clinical data collection, including inter-rater variability in symptom assessment, recall bias in patient reporting, and temporal dynamics of symptom evolution \cite{ref5}.

Third, the study focused on six widely used supervised learning algorithms representing different algorithmic families. While these models span a broad spectrum of complexity and interpretability, more advanced architectures, such as deep convolutional neural networks, recurrent neural networks, or transformer-based models \cite{ref13, ref14, ref15}, were not considered. This exclusion was deliberate, based on their limited applicability in low-resource clinical settings where training data is limited, computational resources are constrained, and model interpretability is paramount \cite{ref26, ref27}. However, it is possible that such advanced architectures might offer performance advantages in settings with larger datasets and greater computational resources.

Fourth, the analysis was retrospective and based on cross-validation using historical clinical data. While cross-validation provides robust estimates of generalization performance \cite{ref29}, prospective validation in real clinical workflows is necessary to assess the true impact of these models on diagnostic decision-making and patient outcomes. The actual clinical utility of the models can only be established through prospective studies that evaluate their impact on diagnostic accuracy, time to diagnosis, treatment decisions, and ultimately patient outcomes such as morbidity and mortality \cite{ref1, ref5}.

Fifth, the study did not address several practical deployment considerations that would be critical for real-world implementation \cite{ref18, ref19}, including integration with existing health information systems, user interface design for clinical decision support, training requirements for healthcare workers, and potential workflow disruptions. Additionally, the analysis did not examine how model performance might degrade over time due to changes in parasite populations, drug resistance patterns \cite{ref9, ref10}, or shifts in clinical presentation, nor did it address strategies for model updating and maintenance in deployed systems. 

Finally, the study focused exclusively on diagnostic classification and did not address related clinical tasks such as severity prediction, treatment response prediction, or risk stratification for complications \cite{ref5}. These related prediction tasks may have different optimization requirements and performance characteristics, limiting the generalizability of findings beyond the specific diagnostic classification context examined here.

\subsection{Future Directions}

Future research should prioritize prospective, multi-center validation studies to evaluate machine learning–based diagnostic support systems under real-world operational conditions \cite{ref18, ref19}. Cluster-randomized trials comparing standard diagnostic practices with ML-augmented workflows would provide robust evidence of clinical utility and cost-effectiveness. Such trials should assess not only diagnostic accuracy but also time to diagnosis, treatment initiation, healthcare worker satisfaction, and patient outcomes including morbidity, mortality, and quality of life \cite{ref1, ref5}.

Methodologically, hybrid optimization approaches that combine the efficiency of random sampling \cite{ref20} with lightweight adaptive mechanisms may offer a promising balance between speed and performance. For example, random search could be used for initial exploration of the hyperparameter space, followed by localized grid refinement around promising configurations. Such hybrid approaches might capture most of the performance benefits of sophisticated methods \cite{ref22, ref24} while maintaining computational efficiency.

Additionally, transfer learning and domain adaptation techniques could mitigate data scarcity by leveraging information from related clinical contexts \cite{ref13, ref14, ref15}. Models trained on large datasets from well-resourced settings might be fine-tuned using smaller datasets from resource-limited settings, potentially improving performance while reducing the data requirements for deployment in new contexts. This approach could be particularly valuable for rare complications or emerging drug-resistant strains \cite{ref9, ref10} where local data may be limited.

From an implementation perspective, the development of healthcare-oriented AutoML frameworks \cite{ref21} tailored to resource-constrained settings could further lower barriers to adoption. Such systems should emphasize transparency, reproducibility, and minimal computational requirements while maintaining regulatory compliance \cite{ref18, ref19}. Ideally, these frameworks would automate the entire pipeline from data preprocessing through model training, optimization, and explainability analysis, while providing interpretable outputs that clinicians can understand and trust.

Future work should also investigate the temporal stability of model performance and develop strategies for model monitoring and updating in deployed systems. As parasite populations evolve, drug resistance patterns change \cite{ref9, ref10}, and clinical presentation characteristics shift, deployed models may experience performance degradation. Research is needed to develop efficient methods for detecting such degradation and updating models with minimal disruption to clinical workflows.

The integration of multiple data modalities, including clinical symptoms, laboratory results, demographic information, and potentially microscopy images \cite{ref13, ref14, ref15}, represents another promising direction. Multimodal approaches might achieve superior performance by leveraging complementary information sources, though this must be balanced against increased data requirements and computational complexity \cite{ref26}. This research is needed to bridge the gap between algorithmic explainability and practical clinical utility of explanations \cite{ref18}. User studies with healthcare workers could examine how different explanation formats influence trust, understanding, and decision-making. This work should inform the design of clinical decision support interfaces that effectively communicate model predictions and supporting evidence in ways that enhance rather than complicate clinical reasoning.

\subsection{ Study Benefits and Public Health Implications}
Malaria remains a major global health challenge, with international targets aiming for substantial reductions in incidence and mortality by 2030 as outlined in the World Health Organization's Global Technical Strategy for Malaria \cite{ref1, ref2}. The findings of this study demonstrate that machine learning–based diagnostic support systems can be developed and deployed without reliance on computationally intensive optimization strategies, making them more accessible for resource-constrained settings where malaria burden is highest \cite{ref26, ref27}. This research investigation offers several important contributions to the literature on machine learning in healthcare and applied biometry:

First, it provides one of the most extensive comparative analyses of hyperparameter optimization strategies conducted specifically within a clinical diagnostic context \cite{ref21}. Unlike prior studies that focus on benchmark datasets or single algorithms, this work evaluates optimization methods across heterogeneous datasets and modeling paradigms, enhancing external validity and providing insights that generalize across different data conditions. The inclusion of both synthetic datasets with controlled complexity and an authentic clinical malaria dataset bridges the gap between methodological benchmarking and real-world applicability.

Second, the study explicitly integrates computational efficiency and stability into the evaluation framework alongside traditional performance metrics. By quantifying evaluations per minute, total optimization time, and variability across replications, it addresses practical considerations that are critical for real-world clinical deployment but often absent from methodological comparisons \cite{ref26, ref27}. This pragmatic focus on deployability distinguishes the work from purely algorithmic studies and provides actionable guidance for practitioners facing resource constraints.

Third, the variance partitioning analysis offers quantitative evidence supporting the primacy of data quality and algorithm selection over optimization method choice \cite{ref29}. This empirical decomposition provides actionable guidance for practitioners on how to allocate modeling effort and resources effectively. Rather than investing heavily in sophisticated optimization infrastructure, the results suggest that efforts should focus on improving data collection protocols, increasing sample sizes, and implementing standardized clinical assessments.

Fourth, the comprehensive explainability analysis using three complementary techniques (LIME, SHAP, PFI) advances beyond typical healthcare ML studies by providing multi-perspective insights into model behavior and feature importance. This approach demonstrates that high-performing models can achieve both strong predictive accuracy and clinical interpretability \cite{ref18}, challenging the false dichotomy often presented between performance and explainability. The consistency of findings across multiple explainability methods strengthens confidence in the identified important features and their clinical relevance.

Fifth, the detailed analysis of class imbalance handling and its impact on model performance provides practical guidance for addressing one of the most common challenges in clinical datasets \cite{ref30}. The demonstrated effectiveness of SMOTE-based oversampling, combined with careful application only within training folds to prevent information leakage, offers a template for rigorous handling of imbalanced data in medical applications.

By documenting the complete analytical pipeline from raw data through preprocessing, model training, optimization, and explainability analysis, the study provides a comprehensive methodological template that can guide future research in clinical machine learning. The emphasis on reproducibility, transparent reporting, and alignment with principles of applied biometry \cite{ref29} makes this work particularly valuable for practitioners seeking to implement similar approaches in other clinical domains.

By enabling rapid model development with modest infrastructure requirements, these results support scalable implementation across primary healthcare networks in endemic regions \cite{ref1, ref3, ref4}. This democratization of diagnostic support technology has the potential to enhance early detection, optimize treatment decisions, and reduce the burden on overstretched healthcare systems. Improved diagnostic accuracy can reduce both under-treatment (with associated morbidity and mortality) and over-treatment (which contributes to drug resistance development \cite{ref9, ref10} and wastes scarce resources). The explainability analyses provide insights that can inform not only automated decision support but also healthcare worker training and clinical guideline development \cite{ref5}. The consistent identification of key predictive features across multiple methods suggests these symptoms should be emphasized in clinical assessment protocols and training programs for community health workers and clinical staff in endemic areas.

Furthermore, the demonstrated feasibility of achieving strong performance with simple optimization methods and moderate computational requirements suggests that even facilities with limited infrastructure can implement sophisticated predictive models \cite{ref26, ref27}. This is particularly important for rural and remote health facilities that may lack reliable electricity or internet connectivity, where model training and deployment must be feasible with basic computational equipment. The potential impact extends beyond individual patient care to public health surveillance and resource allocation. Accurate, scalable diagnostic tools can improve disease monitoring, enable more precise targeting of interventions, and facilitate evaluation of control program effectiveness \cite{ref1, ref2, ref3, ref4}. Machine learning models deployed across multiple facilities could provide real-time surveillance data to guide regional and national malaria control strategies. However, realizing these public health benefits requires addressing implementation challenges including integration with existing health information systems, healthcare worker training, quality assurance mechanisms, and equitable access across different healthcare settings \cite{ref18, ref19, ref26}. The technical feasibility demonstrated in this study represents an important first step, but successful public health impact will require sustained effort in implementation science, health systems strengthening, and policy development.

\declarations

\subsection*{Abbreviations}
Not applicable
\subsection*{Ethics approval and consent to participate}
Not applicable
\subsection*{ Consent for publication}
All authors consented to publish this paper. 
\subsection*{Availability of data and materials}
Code implementing the analyses described in this manuscript will be made available in a public repository upon request.

\subsection*{Competing interests}

The authors declare no competing interests, financial or otherwise, that could have influenced the work reported in this paper.

\subsection*{Funding}

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. The work was conducted as part of the authors' academic and research activities without external financial support.

\subsection*{Authors' contributions}

O.O.A, A.K.B.C. and J.S.S. conceptualized the study and designed the experimental framework. A.K.B.C. implemented the machine learning models and optimization pipelines, conducted the hyperparameter tuning experiments, and generated the performance evaluation results. J.S.S. conducted the statistical analyses, performed the variance decomposition, and led the interpretation of results. J.S.S. also implemented the explainability analyses. O.O.A. supervised the study, contributed to methodological refinement, provided statistical expertise in interpreting model features and results, and ensured alignment with clinical practice considerations. O.O.A2, P.J.O and E.O.O contributed to the writing, literature review, final editing and funding of the paper. All authors contributed to manuscript writing, critically reviewed multiple drafts, and approved the final version for submission. 

\subsection*{Acknowledgments}

The authors acknowledge colleagues in applied biometry and medical informatics for valuable methodological discussions that informed this study and the open-source software development communities whose tools and libraries enabled this work, including the developers of R, Python, and associated machine learning packages.

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