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Learning directed acyclic graphs by determination of candidate causes for discrete variables. (English) Zbl 07193820

Summary: The aim of this paper is learning directed acyclic graph (DAG) by determination of candidate causes for each discrete variable. Based on the fact that the candidate causes of a variable must be a subset of its potential neighbours, we first estimate the potential neighbours for each variable using \(L1\)-regularized Markov blanket. We then introduce a novel scoring function which infers the candidate causes for each variable through its Markov blanket. The lasso regression between each variable (as response variable) and its candidate causes (as predictors) is used to obtain a directed graph. We finally remove the cycles using the simulated annealing (SA) algorithm for achieving a DAG. Experimental results over well-known DAGs indicate that proposed method has higher accuracy and better degree of data matching.

MSC:

62-XX Statistics

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[1] Pearl J.Causal inference without counterfactuals: comment. J Am Stat Assoc. 2000;95(450):407-424. doi: 10.1080/01621459.2000.10474210[Taylor & Francis Online], [Google Scholar]
[2] Bishop CM.Pattern recognition. Mach Learn. 2006;128:1-58. [Google Scholar]
[3] Friedman N, Linial M, Nachman I, et al. Using Bayesian networks to analyze expression data. J Comput Biol. 2000;7(3-4):601-620. doi: 10.1089/106652700750050961[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[4] Sachs K, Perez O, Pe’er D, et al. Causal protein-signaling networks derived from multiparameter single-cell data. Science. 2005;308(5721):523-529. doi: 10.1126/science.1105809[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[5] Neto EC, Keller MP, Attie AD, et al. Causal graphical models in systems genetics: a unified framework for joint inference of causal network and genetic architecture for correlated phenotypes. Ann Appl Stat. 2013;4(1):320. doi: 10.1214/09-AOAS288[Crossref], [Google Scholar] · Zbl 1189.62172
[6] Goudie RJ, Mukherjee S.A Gibbs sampler for learning dags. J Mach Learn Res. 2016;17(2):1-39. [PubMed], [Google Scholar] · Zbl 1360.68677
[7] Koller D, Friedman N. Probabilistic graphical models: principles and techniques. Cambridge, Massachusetts: MIT Press; 2009. [Google Scholar] · Zbl 1183.68483
[8] Pearl J.Probabilistic reasoning in intelligent systems. Br Med J. 1988;308:1591-1596. [Google Scholar]
[9] Schmidt M. Graphical model structure learning using l1-regularization [dissertation]. Vancouver: University of British Columbia; 2010. [Google Scholar]
[10] Tabar VR, Eskandari F, Salimi S, et al. Finding a set of candidate parents using dependency criterion for the k2 algorithm. Pattern Recognit Lett. 2018;111:23-29. doi: 10.1016/j.patrec.2018.04.019[Crossref], [Web of Science ®], [Google Scholar]
[11] Tibshirani R.Regression shrinkage and selection via the lasso. J R Stat Soc Ser B (Methodol). 1996;58(1):267-288. [Crossref], [Google Scholar] · Zbl 0850.62538
[12] Ispolatov I, Maslov S.Detection of the dominant direction of information flow and feedback links in densely interconnected regulatory networks. BMC Bioinf. 2008;9(1):424. doi: 10.1186/1471-2105-9-424[Crossref], [PubMed], [Google Scholar]
[13] Alonso A, Molenberghs G, Burzykowski T, et al. Prentice’s approach and the meta-analytic paradigm: a reflection on the role of statistics in the evaluation of surrogate endpoints. Biometrics. 2004;60(3):724-728. doi: 10.1111/j.0006-341X.2004.00222.x[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1274.62707
[14] Chand S. Goodness of fit tests and lasso variable selection in time series analysis [dissertation]. Nottingham: University of Nottingham; 2011. [Google Scholar]
[15] Efron B, Hastie T, Johnstone I, et al. Least angle regression. Ann Stat. 2004;32(2):407-499. doi: 10.1214/009053604000000067[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1091.62054
[16] Karp RM. Reducibility among combinatorial problems. In: Complexity of computer computations. Springer; 1972. p. 85-103. [Google Scholar] · Zbl 1467.68065
[17] Tarsauliya A, Tiwari R, Shukla A. Financial time series forecast using simulated annealing and threshold acceptance genetic bpa neural network. In: ICEIS (2); 2011. p. 172-177. [Google Scholar]
[18] Tabar VR, Elahi F.A novel method for aggregation of Bayesian networks without considering an ancestral ordering. Appl Artif Intell. 2018;32(2):214-227. doi: 10.1080/08839514.2018.1451134[Taylor & Francis Online], [Web of Science ®], [Google Scholar]
[19] Lauritzen SL, Spiegelhalter DJ.Local computations with probabilities on graphical structures and their application to expert systems. J R Stat Soc Ser B (Methodol). 1988;50(2):157-224. [Google Scholar] · Zbl 0684.68106
[20] Ripley BD. Pattern recognition via neural networks. A volume of Oxford Graduate Lectures on Neural Networks, title to be decided New York Oxford University Press. 1996. [Google Scholar]
[21] Beinlich IA, Suermondt HJ, Chavez RM. The alarm monitoring system: a case study with two probabilistic inference techniques for belief networks. Pittsburgh: Springer; 1989. [Google Scholar]
[22] Fu F. Sparse causal network estimation with experimental intervention. 2012. [Google Scholar]
[23] Tsamardinos I, Brown LE, Aliferis CF.The Max-Min Hill-Climbing Bayesian network structure learning algorithm. Mach Learn. 2006;65(1):31-78. doi: 10.1007/s10994-006-6889-7[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1470.68192
[24] Spirtes P, Glymour CN, Scheines R. Causation, prediction, and search. Cambridge, Massachusetts: MIT Press; 2000. [Google Scholar] · Zbl 0806.62001
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