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A Cooperative Coevolutionary Genetic Algorithm for Learning Bayesian Network Structures

A Cooperative Coevolutionary Genetic Algorithm for Learning Bayesian Network Structures. Arthur Carvalho a3carval@cs.uwaterloo.ca. Outline. Bayesian Networks CCGA Experiments Conclusion. Bayesian Networks. AI technique Diagnosis, predictions, modelling knowledge Graphical model

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A Cooperative Coevolutionary Genetic Algorithm for Learning Bayesian Network Structures

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  1. A Cooperative CoevolutionaryGenetic Algorithm for Learning Bayesian Network Structures Arthur Carvalho a3carval@cs.uwaterloo.ca

  2. Outline • Bayesian Networks • CCGA • Experiments • Conclusion

  3. Bayesian Networks • AI technique • Diagnosis, predictions, modelling knowledge • Graphical model • Represents a joint distribution over a set of random variables • Exploits conditional independence • Concise, natural representation

  4. Bayesian Networks X1 X2 X3

  5. Bayesian Networks X1 X2 X3

  6. Bayesian Networks • Directed acyclic graph (DAG) • Nodes: random variables • Edges: direct influence of one variable on another • Each node is associated with a conditional probability distribution (CPD)

  7. Bayesian Networks • Learning the structure of the network (DAG) • Structure learning problem • Learning parameters that define the CPDs • Parameter estimation • Maximum Likelihood estimation

  8. Bayesian Networks • Structure learning problem in fully observable datasets • Find a DAG that maximizes P(DAG| Data) • [Cooper & Herskovits, 92]

  9. Bayesian Networks • NP-Hard [Chickeringet al, 1994] • The number of possible structures is superexponential in the number of nodes [Robinson, 1977] • For a network with n nodes, the number of different structures is:

  10. Outline • Bayesian Networks • CCGA • Experiments • Conclusion

  11. CCGA • Structure learning task can be decomposed into two dependent subtasks • To find an optimal ordering of the nodes • To find an optimal connectivity matrix

  12. CCGA D B A D C

  13. CCGA D B A D C

  14. CCGA D B A D C

  15. CCGA D B A D C

  16. CCGA D B A A C

  17. CCGA D B A A C

  18. CCGA D B A A C

  19. CCGA D B A B C

  20. CCGA D B A C

  21. CCGA • Two subpopulations • Binary (edges) • Permutation (nodes) • Cooperative Coevolutionary Genetic Algorithm (CCGA) • Each subpopulation is coevolve using a canonical GA

  22. CCGA • Evaluating individual species • Each subpopulation member is combined with both the best known individual and a random individual from the other subpopulation • The fitness function is applied to the two resulting solutions • The highest value is the fitness • CCGA-2 [Potter & De Jong, 1994]

  23. CCGA

  24. Outline • Bayesian Networks • CCGA • Experiments • Conclusion

  25. Experiments • Setup • K2 algorithm [Cooper & Herskovits, 1992] • Alarm network • 37 nodes and 46 edges • Insurance network • 27 nodes and 52 edges • Three datasets • 1000, 3000, and 5000 instances • 100 executions

  26. Experiments • Parameters:

  27. Experiments • Alarm network

  28. Experiments • Insurance network

  29. Outline • Bayesian Networks • CCGA • Experiments • Conclusion

  30. Conclusion • New algorithm to solve the structure learning problem • Novel representation • Good performance • Future work • Incomplete datasets • Graph-related problems

  31. Thank you! Source code and datasets available at: www.cs.uwaterloo.ca/~a3carval/softwares/CCGA_code.rar Arthur Carvalho a3carval@cs.uwaterloo.ca

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