M-GA: A Genetic Algorithm to Search for the Best Conditional Gaussian Bayesian Network

The search of optimal Bayesian network from a database of observations is NP-hard. Nevertheless, several heuristic search strategies have been found to be effective. We present a new population-based algorithm to learn the structure of Bayesian networks without assuming any ordering of nodes and allowing for the presence of both discrete and continuous random variables. Numerical performances of our mixed-genetic algorithm, (M-GA), are investigated on a case study taken from the literature and compared with greedy search

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

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

[3]  Mikhail J. Atallah,et al.  Algorithms and Theory of Computation Handbook , 2009, Chapman & Hall/CRC Applied Algorithms and Data Structures series.

[4]  D. Goldberg,et al.  BOA: the Bayesian optimization algorithm , 1999 .

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

[6]  Claus Dethlefsen,et al.  deal: A Package for Learning Bayesian Networks , 2003 .

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

[8]  Pedro Larrañaga,et al.  Estimation of Distribution Algorithms , 2002, Genetic Algorithms and Evolutionary Computation.

[9]  Susanne Gammelgaard,et al.  Learning conditional Gaussian networks , 2005 .

[10]  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.

[11]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[12]  David Maxwell Chickering,et al.  Learning Bayesian networks: The combination of knowledge and statistical data , 1995, Mach. Learn..

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

[14]  Wai Lam,et al.  LEARNING BAYESIAN BELIEF NETWORKS: AN APPROACH BASED ON THE MDL PRINCIPLE , 1994, Comput. Intell..

[15]  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..

[16]  David Heckerman,et al.  Learning Bayesian Networks: Search Methods and Experimental Results , 1995 .

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

[18]  David J. Spiegelhalter,et al.  Probabilistic Networks and Expert Systems , 1999, Information Science and Statistics.

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

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

[21]  Steffen L. Lauritzen,et al.  Stable local computation with conditional Gaussian distributions , 2001, Stat. Comput..

[22]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems , 1988 .

[23]  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..

[24]  Tom Burr,et al.  Causation, Prediction, and Search , 2003, Technometrics.

[25]  Nir Friedman,et al.  Being Bayesian about Network Structure , 2000, UAI.

[26]  Gregory F. Cooper,et al.  A Bayesian method for the induction of probabilistic networks from data , 1992, Machine Learning.

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

[28]  P. Spirtes,et al.  Causation, Prediction, and Search, 2nd Edition , 2001 .

[29]  Ross Ihaka,et al.  Gentleman R: R: A language for data analysis and graphics , 1996 .

[30]  Jose Miguel Puerta,et al.  Ant colony optimization for learning Bayesian networks , 2002, Int. J. Approx. Reason..

[31]  Robert Castelo,et al.  Improved learning of Bayesian networks , 2001, UAI.

[32]  David Heckerman.  Likelihoods and Parameter Priors for Bayesian Networks , 1995 .

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

[34]  Jin Tian,et al.  A Branch-and-Bound Algorithm for MDL Learning Bayesian Networks , 2000, UAI.

[35]  S. Lauritzen.  Propagation of Probabilities, Means, and Variances in Mixed Graphical Association Models , 1992 .