A review on evolutionary algorithms in Bayesian network learning and inference tasks

Thanks to their inherent properties, probabilistic graphical models are one of the prime candidates for machine learning and decision making tasks especially in uncertain domains. Their capabilities, like representation, inference and learning, if used effectively, can greatly help to build intelligent systems that are able to act accordingly in different problem domains. Bayesian networks are one of the most widely used class of these models. Some of the inference and learning tasks in Bayesian networks involve complex optimization problems that require the use of meta-heuristic algorithms. Evolutionary algorithms, as successful problem solvers, are promising candidates for this purpose. This paper reviews the application of evolutionary algorithms for solving some NP-hard optimization tasks in Bayesian network inference and learning.

[1]  Dirk Thierens,et al.  On the Use of a Non-redundant Encoding for Learning Bayesian Networks from Data with a GA , 2004, PPSN.

[2]  Kay Chen Tan,et al.  Evolutionary Multi-objective Optimization in Uncertain Environments - Issues and Algorithms , 2009, Studies in Computational Intelligence.

[3]  Pedro Larrañaga,et al.  Probabilistic graphical models in artificial intelligence , 2011, Appl. Soft Comput..

[4]  Thomas G. Dietterich.  Adaptive computation and machine learning , 1998 .

[5]  Gregory F. Cooper,et al.  The Computational Complexity of Probabilistic Inference Using Bayesian Belief Networks , 1990, Artif. Intell..

[6]  Risto Miikkulainen,et al.  Competitive Coevolution through Evolutionary Complexification , 2011, J. Artif. Intell. Res..

[7]  Paul A. Viola,et al.  MIMIC: Finding Optima by Estimating Probability Densities , 1996, NIPS.

[8]  John R. Koza,et al.  Genetic Programming IV: Routine Human-Competitive Machine Intelligence , 2003 .

[9]  Jonathan Timmis,et al.  Artificial immune systems - a new computational intelligence paradigm , 2002 .

[10]  P. Nordin.  Genetic Programming III - Darwinian Invention and Problem Solving , 1999 .

[11]  J. A. Lozano,et al.  Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation , 2001 .

[12]  R. K. Ursem.  Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[13]  Tharam S. Dillon,et al.  An improved naive Bayesian classifier technique coupled with a novel input solution method [rainfall prediction] , 2001, IEEE Trans. Syst. Man Cybern. Syst..

[14]  Max Henrion,et al.  Propagating uncertainty in bayesian networks by probabilistic logic sampling , 1986, UAI.

[15]  G. Casella,et al.  Explaining the Gibbs Sampler , 1992 .

[16]  Qiang Shen,et al.  Learning Bayesian networks: approaches and issues , 2011, The Knowledge Engineering Review.

[17]  Martin Pelikan,et al.  Hierarchical Bayesian optimization algorithm: toward a new generation of evolutionary algorithms , 2010, SICE 2003 Annual Conference (IEEE Cat. No.03TH8734).

[18]  Kwong-Sak Leung,et al.  Using Evolutionary Programming and Minimum Description Length Principle for Data Mining of Bayesian Networks , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  Ross D. Shachter,et al.  Simulation Approaches to General Probabilistic Inference on Belief Networks , 2013, UAI.

[20]  Pedro Larrañaga,et al.  Triangulation of Bayesian networks with recursive estimation of distribution algorithms , 2009, Int. J. Approx. Reason..

[21]  Dirk Thierens,et al.  Building a GA from Design Principles for Learning Bayesian Networks , 2003, GECCO.

[22]  Doug Fisher,et al.  Learning from Data: Artificial Intelligence and Statistics V , 1996 .

[23]  E. Cantu-Paz,et al.  The Gambler's Ruin Problem, Genetic Algorithms, and the Sizing of Populations , 1997, Evolutionary Computation.

[24]  Kwong-Sak Leung,et al.  An efficient data mining method for learning Bayesian networks using an evolutionary algorithm-based hybrid approach , 2004, IEEE Transactions on Evolutionary Computation.

[25]  Constantin F. Aliferis,et al.  The max-min hill-climbing Bayesian network structure learning algorithm , 2006, Machine Learning.

[26]  A. Dawid.  Conditional Independence in Statistical Theory , 1979 .

[27]  David E. Goldberg,et al.  The gambler''s ruin problem , 1997 .

[28]  Richard E. Neapolitan,et al.  Learning Bayesian networks , 2007, KDD '07.

[29]  H. Muhlenbein,et al.  The Factorized Distribution Algorithm for additively decomposed functions , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[30]  Kwong-Sak Leung,et al.  Data mining of Bayesian networks using cooperative coevolution , 2004, Decis. Support Syst..

[31]  Stuart J. Russell,et al.  Dynamic bayesian networks: representation, inference and learning , 2002 .

[32]  Shumeet Baluja,et al.  Using Optimal Dependency-Trees for Combinational Optimization , 1997, ICML.

[33]  Jérôme Habrant,et al.  Structure Learning of Bayesian Networks from Databases by Genetic Algorithms-Application to Time Series Prediction in Finance , 1999, ICEIS.

[34]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[35]  Mitsuo Gen,et al.  Genetic Algorithms , 1999, Wiley Encyclopedia of Computer Science and Engineering.

[36]  Jarmo T. Alander,et al.  An Indexed Bibliography of Genetic Algorithms in Medicine , 2014 .

[37]  Wray L. Buntine.  Theory Refinement on Bayesian Networks , 1991, UAI.

[38]  Wray L. Buntine.  A Guide to the Literature on Learning Probabilistic Networks from Data , 1996, IEEE Trans. Knowl. Data Eng..

[39]  Federico M. Stefanini,et al.  M-GA: A Genetic Algorithm to Search for the Best Conditional Gaussian Bayesian Network , 2005, International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC'06).

[40]  Nichael Lynn Cramer,et al.  A Representation for the Adaptive Generation of Simple Sequential Programs , 1985, ICGA.

[41]  Peng Yu,et al.  Learning dynamic Bayesian network with immune evolutionary algorithm , 2005, 2005 International Conference on Machine Learning and Cybernetics.

[42]  Adnan Darwiche,et al.  Modeling and Reasoning with Bayesian Networks , 2009 .

[43]  Edzard S. Gelsema,et al.  Abductive reasoning in Bayesian belief networks using a genetic algorithm , 1995, Pattern Recognit. Lett..

[44]  R. W. Robinson.  Counting unlabeled acyclic digraphs , 1977 .

[45]  María S. Pérez-Hernández,et al.  Learning Semi Naïve Bayes Structures by Estimation of Distribution Algorithms , 2003, EPIA.

[46]  Hao Wang,et al.  Triangulation of Bayesian Networks Using an Adaptive Genetic Algorithm , 2006, ISMIS.

[47]  William H. Hsu,et al.  A Permutation Genetic Algorithm For Variable Ordering In Learning Bayesian Networks From Data , 2002, GECCO.

[48]  R. van Engelen,et al.  Approximating Bayesian belief networks by arc removal , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[49]  C. Cotta.  On the Learning of Bayesian Network Graph Structures via Evolutionary Programming , 2004 .

[50]  Peter Gr Unwald.  The minimum description length principle and reasoning under uncertainty , 1998 .

[51]  Goldberg,et al.  Genetic algorithms , 1993, Robust Control Systems with Genetic Algorithms.

[52]  David E. Goldberg,et al.  The Design of Innovation: Lessons from and for Competent Genetic Algorithms , 2002 .

[53]  Edmund K. Burke,et al.  The Cooperative Royal Road: Avoiding Hitchhiking , 2007, Artificial Evolution.

[54]  Brian J. Ross,et al.  Evolving dynamic Bayesian networks with Multi-objective genetic algorithms , 2007, Applied Intelligence.

[55]  Pedro Larrañaga,et al.  Towards a New Evolutionary Computation - Advances in the Estimation of Distribution Algorithms , 2006, Towards a New Evolutionary Computation.

[56]  Evelyne Lutton,et al.  Bayesian network structure learning using cooperative coevolution , 2009, GECCO.

[57]  Kathryn B. Laskey,et al.  Learning Bayesian networks from incomplete data using evolutionary algorithms , 1999 .

[58]  John A. W. McCall,et al.  Evolved bayesian networks as a versatile alternative to partin tables for prostate cancer management , 2008, GECCO '08.

[59]  David Maxwell Chickering,et al.  Large-Sample Learning of Bayesian Networks is NP-Hard , 2002, J. Mach. Learn. Res..

[60]  Finn V. Jensen,et al.  Bayesian Networks and Decision Graphs , 2001, Statistics for Engineering and Information Science.

[61]  Michael J. Pazzani,et al.  Searching for Dependencies in Bayesian Classifiers , 1995, AISTATS.

[62]  María S. Pérez-Hernández,et al.  Bayesian network multi-classifiers for protein secondary structure prediction , 2004, Artif. Intell. Medicine.

[63]  ROSA BLANCO,et al.  Gene Selection For Cancer Classification Using Wrapper Approaches , 2004, Int. J. Pattern Recognit. Artif. Intell..

[64]  Zhen Li,et al.  Classifier Learning Algorithm Based on Genetic Algorithms , 2007, Second International Conference on Innovative Computing, Informatio and Control (ICICIC 2007).

[65]  Pedro Larrañaga,et al.  Unsupervised Learning Of Bayesian Networks Via Estimation Of Distribution Algorithms: An Application To Gene Expression Data Clustering , 2004, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[66]  David Heckerman,et al.  A Tutorial on Learning with Bayesian Networks , 1998, Learning in Graphical Models.

[67]  Judea Pearl,et al.  Distributed Revision of Composite Beliefs , 1987, Artif. Intell..

[68]  David C. Wilkins,et al.  Efficient Bayesian Network Inference: Genetic Algorithms, Stochastic Local Search, and Abstraction , 1999 .

[69]  Pedro Larrañaga,et al.  Learning Bayesian Networks In The Space Of Orderings With Estimation Of Distribution Algorithms , 2004, Int. J. Pattern Recognit. Artif. Intell..

[70]  Nir Friedman,et al.  Probabilistic Graphical Models - Principles and Techniques , 2009 .

[71]  John R. Koza,et al.  Genetic programming - on the programming of computers by means of natural selection , 1993, Complex adaptive systems.

[72]  John R. Koza,et al.  Genetic Programming III: Darwinian Invention & Problem Solving , 1999 .

[73]  G. Bortolan,et al.  The problem of linguistic approximation in clinical decision making , 1988, Int. J. Approx. Reason..

[74]  LarrañagaPedro,et al.  A review on evolutionary algorithms in Bayesian network learning and inference tasks , 2013 .

[75]  B. C. Brookes,et al.  Information Sciences , 2020, Cognitive Skills You Need for the 21st Century.

[76]  Pedro Larrañaga,et al.  Machine Learning : Editorial , 2005 .

[77]  Wilson X. Wen,et al.  Optimal decomposition of belief networks , 1990, UAI.

[78]  H. Mühlenbein,et al.  From Recombination of Genes to the Estimation of Distributions I. Binary Parameters , 1996, PPSN.

[79]  Pedro Larrañaga,et al.  Feature subset selection by Bayesian networks: a comparison with genetic and sequential algorithms , 2001, Int. J. Approx. Reason..

[80]  Luis M. de Campos,et al.  Partial Abductive Inference in Bayesian Networks: An Empirical Comparison Between GAs and EDAs , 2002, Estimation of Distribution Algorithms.

[81]  Pedro Larrañaga,et al.  Structure Learning of Bayesian Networks by Hybrid Genetic Algorithms , 1995, AISTATS.

[82]  Shasha Feng,et al.  A Stable Stochastic Optimization Algorithm for Triangulation of Bayesian Networks , 2010, 2010 Third International Conference on Knowledge Discovery and Data Mining.

[83]  J. Rissanen,et al.  Modeling By Shortest Data Description* , 1978, Autom..

[84]  Mitsuo Gen,et al.  Genetic algorithms and engineering optimization , 1999 .

[85]  Pedro Larrañaga,et al.  Using Bayesian networks in the construction of a bi-level multi-classifier. A case study using intensive care unit patients data , 2001, Artif. Intell. Medicine.

[86]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[87]  A. Darwiche,et al.  Complexity Results and Approximation Strategies for MAP Explanations , 2011, J. Artif. Intell. Res..

[88]  R. Bouckaert.  Bayesian belief networks : from construction to inference , 1995 .

[89]  Uffe Kjærulff.  Optimal decomposition of probabilistic networks by simulated annealing , 1992 .

[90]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[91]  H. Akaike.  A new look at the statistical model identification , 1974 .

[92]  Pedro Larrañaga,et al.  Learning Bayesian network structures by searching for the best ordering with genetic algorithms , 1996, IEEE Trans. Syst. Man Cybern. Part A.

[93]  Pedro Larrañaga,et al.  Learning Bayesian networks in the space of structures by estimation of distribution algorithms , 2003, Int. J. Intell. Syst..

[94]  P. Spirtes,et al.  An Algorithm for Fast Recovery of Sparse Causal Graphs , 1991 .

[95]  Nir Friedman,et al.  Bayesian Network Classifiers , 1997, Machine Learning.

[96]  Serafín Moral,et al.  Novel strategies to approximate probability trees in penniless propagation , 2003, Int. J. Intell. Syst..

[97]  Pedro Larrañaga,et al.  Structure Learning of Bayesian Networks by Genetic Algorithms: A Performance Analysis of Control Parameters , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[98]  David E. Goldberg,et al.  A Survey of Optimization by Building and Using Probabilistic Models , 2002, Comput. Optim. Appl..

[99]  Solomon Eyal Shimony,et al.  Finding MAPs for Belief Networks is NP-Hard , 1994, Artif. Intell..

[100]  Carlos Cotta,et al.  A Primer on the Evolution of Equivalence Classes of Bayesian-Network Structures , 2004, PPSN.

[101]  Pedro Larrañaga,et al.  Feature Subset Selection by Bayesian network-based optimization , 2000, Artif. Intell..

[102]  S. Chib,et al.  Understanding the Metropolis-Hastings Algorithm , 1995 .

[103]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[104]  Enrique F. Castillo,et al.  Expert Systems and Probabilistic Network Models , 1996, Monographs in Computer Science.

[105]  Bruce Abramson,et al.  The Topological Fusion of Bayes Nets , 1992, UAI.

[106]  David E. Goldberg,et al.  The compact genetic algorithm , 1999, IEEE Trans. Evol. Comput..

[107]  Pedro Larrañaga,et al.  Feature subset selection by genetic algorithms and estimation of distribution algorithms - A case study in the survival of cirrhotic patients treated with TIPS , 2001, Artif. Intell. Medicine.

[108]  Xiaohui Liu,et al.  Spatial Operators for Evolving Dynamic Bayesian Networks from Spatio-temporal Data , 2003, GECCO.

[109]  Mark A. Kramer,et al.  An Evolutionary Computing Approach to Probabilistic Reasoning on Bayesian Networks , 1996, Evolutionary Computation.

[110]  David Maxwell Chickering,et al.  Learning Bayesian Networks is NP-Complete , 2016, AISTATS.

[111]  Euntai Kim,et al.  Structure Learning of Bayesian Networks Using Dual Genetic Algorithm , 2008, IEICE Trans. Inf. Syst..

[112]  John J. Grefenstette,et al.  A Coevolutionary Approach to Learning Sequential Decision Rules , 1995, ICGA.

[113]  S. Auwatanamongkol,et al.  On Approximating K-MPE of Bayesian Networks Using Genetic Algorithm , 2006, 2006 IEEE Conference on Cybernetics and Intelligent Systems.

[114]  David Maxwell Chickering,et al.  Learning Equivalence Classes of Bayesian Network Structures , 1996, UAI.

[115]  Shumeet Baluja,et al.  A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning , 1994 .

[116]  Mehran Sahami,et al.  Learning Limited Dependence Bayesian Classifiers , 1996, KDD.

[117]  J. A. Lozano,et al.  Towards a New Evolutionary Computation: Advances on Estimation of Distribution Algorithms (Studies in Fuzziness and Soft Computing) , 2006 .

[118]  Pedro Larrañaga,et al.  Analysis of the behaviour of genetic algorithms when learning Bayesian network structure from data , 1997, Pattern Recognit. Lett..

[119]  Christopher Kabrhel,et al.  Derivation and validation of a Bayesian network to predict pretest probability of venous thromboembolism. , 2004, Annals of emergency medicine.

[120]  Zexuan Zhu,et al.  Markov blanket-embedded genetic algorithm for gene selection , 2007, Pattern Recognit..

[121]  Haiyang Jia,et al.  Learning Markov equivalence classes of Bayesian Network with immune genetic algorithm , 2008, 2008 3rd IEEE Conference on Industrial Electronics and Applications.

[122]  Franz von Kutschera,et al.  Causation , 1993, J. Philos. Log..

[123]  Frank Jensen,et al.  Approximations in Bayesian Belief Universe for Knowledge Based Systems , 2013, UAI 1990.

[124]  John A. W. McCall,et al.  A chain-model genetic algorithm for Bayesian network structure learning , 2007, GECCO '07.

[125]  W. Vent,et al.  Rechenberg, Ingo, Evolutionsstrategie — Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. 170 S. mit 36 Abb. Frommann‐Holzboog‐Verlag. Stuttgart 1973. Broschiert , 1975 .

[126]  Pedro Larrañaga,et al.  Decomposing Bayesian networks: triangulation of the moral graph with genetic algorithms , 1997, Stat. Comput..

[127]  Lawrence J. Fogel,et al.  Artificial Intelligence through Simulated Evolution , 1966 .

[128]  José A. Gámez,et al.  Partial abductive inference in Bayesian belief networks using a genetic algorithm , 1999, Pattern Recognit. Lett..

[129]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[130]  David Maxwell Chickering,et al.  Learning Bayesian Networks: The Combination of Knowledge and Statistical Data , 1994, Machine Learning.

[131]  Gregory F. Cooper,et al.  A Bayesian Method for the Induction of Probabilistic Networks from Data , 1992 .

[132]  David Heckerman,et al.  Learning Gaussian Networks , 1994, UAI.

[133]  William E. Hart,et al.  Memetic Evolutionary Algorithms , 2005 .

[134]  Pedro Larrañaga,et al.  Predicting survival in malignant skin melanoma using Bayesian networks automatically induced by genetic algorithms. An empirical comparison between different approaches , 1998, Artif. Intell. Medicine.

[135]  David J. Spiegelhalter,et al.  Local computations with probabilities on graphical structures and their application to expert systems , 1990 .

[136]  John R. Koza,et al.  Genetic programming 2 - automatic discovery of reusable programs , 1994, Complex Adaptive Systems.

[137]  Marvin Minsky,et al.  Steps toward Artificial Intelligence , 1995, Proceedings of the IRE.

[138]  Dan Dumitrescu,et al.  Prüfer Number Encoding for Genetic Bayesian Network Structure Learning Algorithm , 2008, 2008 10th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing.

[139]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[140]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[141]  Pedro Larrañaga,et al.  Wrapper discretization by means of estimation of distribution algorithms , 2007, Intell. Data Anal..

[142]  Robert Castelo,et al.  On Inclusion-Driven Learning of Bayesian Networks , 2003, J. Mach. Learn. Res..

[143]  Carlos Cotta,et al.  Towards a More Efficient Evolutionary Induction of Bayesian Networks , 2002, PPSN.

[144]  Xiaohui Liu,et al.  Evolutionary learning of dynamic probabilistic models with large time lags , 2001, Int. J. Intell. Syst..

[145]  Ingo Rechenberg,et al.  Evolutionsstrategie : Optimierung technischer Systeme nach Prinzipien der biologischen Evolution , 1973 .

[146]  Sung-Bae Cho,et al.  Robust Inference of Bayesian Networks Using Speciated Evolution and Ensemble , 2005, ISMIS.

[147]  Nir Friedman,et al.  Probabilistic Graphical Models: Principles and Techniques - Adaptive Computation and Machine Learning , 2009 .

[148]  Jonathan Timmis,et al.  Artificial Immune Systems: A New Computational Intelligence Approach , 2003 .

[149]  D. Nilsson,et al.  An efficient algorithm for finding the M most probable configurationsin probabilistic expert systems , 1998, Stat. Comput..

[150]  N. Wermuth,et al.  Graphical Models for Associations between Variables, some of which are Qualitative and some Quantitative , 1989 .