@inproceedings{Silander,
author = {Silander, Tomi and Myllym\"{a}ki, Petri},
title = {A Simple Approach for Finding the Globally Optimal Bayesian Network Structure},
year = {2006},
isbn = {0974903922},
publisher = {AUAI Press},
address = {Arlington, Virginia, USA},
booktitle = {Proceedings of the Twenty-Second Conference on Uncertainty in Artificial Intelligence},
pages = {445–452},
numpages = {8},
location = {Cambridge, MA, USA},
series = {UAI’06}
}

@article{Singh,
author = "Ajit P. Singh and Andrew W. Moore",
title = "{Finding optimal Bayesian networks by dynamic programming}",
year = "2018",
url = {https://kilthub.cmu.edu/articles/journal_contribution/Finding_optimal_Bayesian_networks_by_dynamic_programming/6605669},
doi = {https://doi.org/10.1184/R1/6605669.v1}
}

@article{gob,
author = {Bartlett, Mark and Cussens, James},
year = {2015},
month = {03},
pages = {},
title = {Integer Linear Programming for the Bayesian network structure learning problem},
volume = {11},
journal = {Artificial Intelligence},
doi = {10.1016/j.artint.2015.03.003}
}

@article{MILLSTEIN20201240,
title = "Prognostic gene expression signature for high-grade serous ovarian cancer",
journal = "Annals of Oncology",
volume = "31",
number = "9",
pages = "1240 - 1250",
year = "2020",
issn = "0923-7534",
doi = "https://doi.org/10.1016/j.annonc.2020.05.019",
url = "http://www.sciencedirect.com/science/article/pii/S0923753420398410",
author = {J. Millstein and T. Budden and E.L. Goode and others}
}

@book{darwiche_2009, place={Cambridge}, title={Modeling and Reasoning with Bayesian Networks}, DOI={10.1017/CBO9780511811357}, publisher={Cambridge University Press}, author={Darwiche, Adnan}, year={2009}}

@article{Chickering2004,
author = {Chickering, David Maxwell and Heckerman, David and Meek, Christopher},
title = {Large-Sample Learning of Bayesian Networks is NP-Hard},
year = {2004},
issue_date = {12/1/2004},
publisher = {JMLR.org},
volume = {5},
issn = {1532-4435},
abstract = {In this paper, we provide new complexity results for algorithms that learn discrete-variable Bayesian networks from data. Our results apply whenever the learning algorithm uses a scoring criterion that favors the simplest structure for which the model is able to represent the generative distribution exactly. Our results therefore hold whenever the learning algorithm uses a consistent scoring criterion and is applied to a sufficiently large dataset. We show that identifying high-scoring structures is NP-hard, even when any combination of one or more of the following hold: the generative distribution is perfect with respect to some DAG containing hidden variables; we are given an independence oracle; we are given an inference oracle; we are given an information oracle; we restrict potential solutions to structures in which each node has at most k parents, for all k&gt;=3.Our proof relies on a new technical result that we establish in the appendices. In particular, we provide a method for constructing the local distributions in a Bayesian network such that the resulting joint distribution is provably perfect with respect to the structure of the network.},
journal = {J. Mach. Learn. Res.},
month = dec,
pages = {1287–1330},
numpages = {44}
}

@article{BN_Ainsworth,
author ={Ainsworth, Holly F and others},
title = {A comparison of methods for inferring causal relationships between genotype and phenotype using additional biological measurements. Genetic epidemiology vol. 41,7 (2017): 577-586. doi:10.1002/gepi.22061},
doi = {10.1002/gepi.22061}
}

@MISC{Carvalho09scoringfunctions,
    author = {Alexandra M. Carvalho},
    title = {Scoring functions for learning Bayesian networks},
    year = {2009}
}

@inproceedings{bgeBase,
author = {Geiger, Dan and Heckerman, David},
title = {Learning Gaussian Networks},
year = {1994},
isbn = {1558603328},
publisher = {Morgan Kaufmann Publishers Inc.},
address = {San Francisco, CA, USA},
abstract = {We describe scoring metrics for learning Bayesian networks from a combination of user knowledge and statistical data. Previous work has concentrated on metrics for domains containing only discrete variables, under the assumption that data represents a multinomial sample. In this paper, we extend this work, developing scoring metrics for domains containing only continuous variables under the assumption that continuous data is sampled from a multivariate normal distribution. Our work extends traditional statistical approaches for identifying vanishing regression coefficients in that we identify two important assumptions, called event equivalence and parameter modularity, that when combined allow the construction of prior distributions for multivariate normal parameters from a single prior Bayesian network specified by a user.},
booktitle = {Proceedings of the Tenth International Conference on Uncertainty in Artificial Intelligence},
pages = {235–243},
numpages = {9},
location = {Seattle, WA},
series = {UAI'94}
}

@article{bicBase,
author = "Schwarz, Gideon",
doi = "10.1214/aos/1176344136",
fjournal = "Annals of Statistics",
journal = "Ann. Statist.",
month = "03",
number = "2",
pages = "461--464",
publisher = "The Institute of Mathematical Statistics",
title = "Estimating the Dimension of a Model",
url = "https://doi.org/10.1214/aos/1176344136",
volume = "6",
year = "1978"
}


@article{bgeAdd,
author = "Kuipers, Jack and Moffa, Giusi and Heckerman, David",
doi = "10.1214/14-AOS1217",
fjournal = "Annals of Statistics",
journal = "Ann. Statist.",
month = "08",
number = "4",
pages = "1689--1691",
publisher = "The Institute of Mathematical Statistics",
title = "Addendum on the scoring of Gaussian directed acyclic graphical models",
url = "https://doi.org/10.1214/14-AOS1217",
volume = "42",
year = "2014"
}

@ARTICLE{appNeuro,
  
AUTHOR={Bielza, Concha and Larrañaga, Pedro},   
	 
TITLE={Bayesian networks in neuroscience: a survey},      
	
JOURNAL={Frontiers in Computational Neuroscience},      
	
VOLUME={8},      

PAGES={131},     
	
YEAR={2014},      
	  
URL={https://www.frontiersin.org/article/10.3389/fncom.2014.00131},       
	
DOI={10.3389/fncom.2014.00131},      
	
ISSN={1662-5188},   
   
}

@inproceedings{ExpressionApp,
author = {Friedman, Nir and Linial, Michal and Nachman, Iftach and Pe'er, Dana},
title = {Using Bayesian Networks to Analyze Expression Data},
year = {2000},
isbn = {1581131860},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
url = {https://doi.org/10.1145/332306.332355},
doi = {10.1145/332306.332355},
booktitle = {Proceedings of the Fourth Annual International Conference on Computational Molecular Biology},
pages = {127–135},
numpages = {9},
location = {Tokyo, Japan},
series = {RECOMB '00}
}

@ARTICLE{appDis1,
author={Agrahari, Rupesh
and Foroushani, Amir
and Docking, T. Roderick
and Chang, Linda
and Duns, Gerben
and Hudoba, Monika
and Karsan, Aly
and Zare, Habil},
title={Applications of Bayesian network models in predicting types of hematological malignancies},
journal={Scientific Reports},
year={2018},
month={May},
day={03},
volume={8},
number={1},
pages={6951},

issn={2045-2322},
doi={10.1038/s41598-018-24758-5},
url={https://doi.org/10.1038/s41598-018-24758-5}
}

@Article{AppGenes,
author={Su, Chengwei
and Andrew, Angeline
and Karagas, Margaret R.
and Borsuk, Mark E.},
title={Using Bayesian networks to discover relations between genes, environment, and disease},
journal={BioData Mining},
year={2013},
month={Mar},
day={21},
volume={6},
number={1},
pages={6},
issn={1756-0381},
doi={10.1186/1756-0381-6-6},
url={https://doi.org/10.1186/1756-0381-6-6}
}

@Article{HCref,
author={Margaritis D},
title={Learning Bayesian network model structure from data, PhD thesis. Pittsburgh: Carnegie-Mellon
University, School of Computer Science},
year={2003}
}

@Article{MMHCCref,
author={Tsamardinos, Ioannis
and Brown, Laura E.
and Aliferis, Constantin F.},
title={The max-min hill-climbing Bayesian network structure learning algorithm},
journal={Machine Learning},
year={2006},
month={Oct},
day={01},
volume={65},
number={1},
pages={31-78},
issn={1573-0565},
doi={10.1007/s10994-006-6889-7},
url={https://doi.org/10.1007/s10994-006-6889-7}
}

@article{Koivisto2004ExactBS,
  title={Exact Bayesian Structure Discovery in Bayesian Networks},
  author={M. Koivisto and K. Sood},
  journal={J. Mach. Learn. Res.},
  year={2004},
  volume={5},
  pages={549-573}
}


@Book{bnBookKorb,
author = { Korb, Kevin B. and Nicholson, Ann E. },
title = { Bayesian artificial intelligence},
isbn = { 1584883871 },
publisher = { Chapman \& Hall/CRC Boca Raton, FL },
pages = { 364 p. : },
year = { 2004 },
type = { Book },
language = { English },
subjects = { Bayesian statistical decision theory -- Data processing.; Machine learning.; Neural networks (Computer science) },
life-dates = { 2004 -  },
}

@article{bnlearn_Scutari,
   author = {Marco Scutari},
   title = {Learning Bayesian Networks with the bnlearn R Package},
   journal = {Journal of Statistical Software, Articles},
   volume = {35},
   number = {3},
   year = {2010},
   keywords = {},
   abstract = {bnlearn is an R package (R Development Core Team 2010) which includes several algorithms for learning the structure of Bayesian networks with either discrete or continuous variables. Both constraint-based and score-based algorithms are implemented, and can use the functionality provided by the snow package (Tierney et al. 2008) to improve their performance via parallel computing. Several network scores and conditional independence algorithms are available for both the learning algorithms and independent use. Advanced plotting options are provided by the Rgraphviz package (Gentry et al. 2010).},
   issn = {1548-7660},
   pages = {1--22},
   doi = {10.18637/jss.v035.i03},
   url = {https://www.jstatsoft.org/v035/i03}
}

@article{scoresComparision,
   author = {Liu, Z. and Malone, B. and Yuan, C.},
   title = {Empirical evaluation of scoring functions for Bayesian network model selection},
   journal = {BMC Bioinformatics},
   volume = {13},
   number = {S14},
   year = {2012},
   keywords = {},
   url = {https://doi.org/10.1186/1471-2105-13-S15-S14}
}

@inproceedings{parentsidentAlgo,
 author = {Scanagatta, Mauro and de Campos, Cassio P and Corani, Giorgio and Zaffalon, Marco},
 booktitle = {Advances in Neural Information Processing Systems},
 editor = {C. Cortes and N. Lawrence and D. Lee and M. Sugiyama and R. Garnett},
 pages = {},
 publisher = {Curran Associates, Inc.},
 title = {Learning Bayesian Networks with Thousands of Variables},
 url = {https://proceedings.neurips.cc/paper/2015/file/2b38c2df6a49b97f706ec9148ce48d86-Paper.pdf},
 volume = {28},
 year = {2015}
}

@inproceedings{Koivisto2,
author = {Koivisto, Mikko},
title = {Advances in Exact Bayesian Structure Discovery in Bayesian Networks},
year = {2006},
isbn = {0974903922},
publisher = {AUAI Press},
address = {Arlington, Virginia, USA},
abstract = {We consider a Bayesian method for learning the Bayesian network structure from complete data. Recently, Koivisto and Sood (2004) presented an algorithm that for any single edge computes its marginal posterior probability in O(n2n) time, where n is the number of attributes; the number of parents per attribute is bounded by a constant. In this paper we show that the posterior probabilities for all the n(n - 1) potential edges can be computed in O(n2n) total time. This result is achieved by a forward-backward technique and fast M\"{o}bius transform algorithms, which are of independent interest. The resulting speedup by a factor of about n2 allows us to experimentally study the statistical power of learning moderate-size networks. We report results from a simulation study that covers data sets with 20 to 10,000 records over 5 to 25 discrete attributes.},
booktitle = {Proceedings of the Twenty-Second Conference on Uncertainty in Artificial Intelligence},
pages = {241–248},
numpages = {8},
location = {Cambridge, MA, USA},
series = {UAI'06}
}

@article{CHENG200243,
title = {Learning Bayesian networks from data: An information-theory based approach},
journal = {Artificial Intelligence},
volume = {137},
number = {1},
pages = {43-90},
year = {2002},
issn = {0004-3702},
doi = {https://doi.org/10.1016/S0004-3702(02)00191-1},
url = {https://www.sciencedirect.com/science/article/pii/S0004370202001911},
author = {Jie Cheng and Russell Greiner and Jonathan Kelly and David Bell and Weiru Liu},
keywords = {Bayesian belief nets, Learning, Probabilistic model, Knowledge discovery, Data mining, Conditional independence test, Monotone DAG-faithful, Information theory},
abstract = {This paper provides algorithms that use an information-theoretic analysis to learn Bayesian network structures from data. Based on our three-phase learning framework, we develop efficient algorithms that can effectively learn Bayesian networks, requiring only polynomial numbers of conditional independence (CI) tests in typical cases. We provide precise conditions that specify when these algorithms are guaranteed to be correct as well as empirical evidence (from real world applications and simulation tests) that demonstrates that these systems work efficiently and reliably in practice.}
}

@article {Collins2020,
	author = {Collins, Rachel and Fenton, Norman},
	title = {Bayesian network modelling for early diagnosis and prediction of Endometriosis},
	elocation-id = {2020.11.04.20225946},
	year = {2020},
	doi = {10.1101/2020.11.04.20225946},
	publisher = {Cold Spring Harbor Laboratory Press},
	URL = {https://www.medrxiv.org/content/early/2020/11/06/2020.11.04.20225946},
	eprint = {https://www.medrxiv.org/content/early/2020/11/06/2020.11.04.20225946.full.pdf},
	journal = {medRxiv}
}

@ARTICLE{mmhc,
  author        = {I. Tsamardinos and L. E. Brown and C. F. Aliferis},
  title         = {{The Max-Min Hill-Climbing Bayesian Network Structure Learning Algorithm}},
  journal       = {Machine Learning},
  volume        = {65},
  number        = {1},
  year          = {2006},
  pages         = {31--78}
}

@ARTICLE{jstatsoft09,
  title         = {{Learning Bayesian Networks with the bnlearn R Package}},
  author        = {M. Scutari},
  journal       = {Journal of Statistical Software},
  year          = {2010},
  volume        = {35},
  number        = {3},
  pages         = {1--22},
  url           = {http://www.jstatsoft.org/v35/i03/}
}

@inproceedings{FDR,
  title={Recent Advances in Biostatistics: False Discovery Rates, Survival Analysis, and Related Topics},
  author={Manish C. Bhattacharjee and Sunil K. Dhar and Sundarraman Subramanian},
  year={2011}
}

@article{hamm1,
author = {Butts, Carter and Carley, Kathleen},
year = {2005},
month = {12},
pages = {291-305},
title = {Some Simple Algorithms for Structural Comparison},
volume = {11},
journal = {Computational \& Mathematical Organization Theory},
doi = {10.1007/s10588-005-5586-6}
}

@ARTICLE{hamm2,
  author={Hamming, R. W.},
  journal={The Bell System Technical Journal}, 
  title={Error detecting and error correcting codes}, 
  year={1950},
  volume={29},
  number={2},
  pages={147-160},
  doi={10.1002/j.1538-7305.1950.tb00463.x}}