Bayesian scoring functions for Bayesian Belief Networks

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Covers the BD, BDe, BDeu, and K2 Bayesian scoring functions for Bayesian Belief Networks (BBNs)

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Bayesian scoring functions for Bayesian Belief Networks

  1. 1. BAYESIANSCORINGFUNCTIONS FORBAYESIAN BELIEFNETWORKS (BBNS)Jee Vang, vangjee@gmail.comVersion 3.1This work is licensed under a Creative Commons Attribution 3.0Unported License.
  2. 2. PURPOSE AND OUTLINE Purpose: concisely illustrate how some Bayesian scoringfunctions have been established to score Bayesian beliefnetworks (BBNs) Define a BBN Cover what Bayesian scoring functions are based on Basic mathematic functions (factorial, gamma, and Beta functions) Probability distributions (multinomial, Dirichlet, Dirichlet-multinomial) Bayes’ Theorem Assumptions Give a few Bayesian scoring function examples (BD, K2, BDe,BDeu)THIS W ORK IS LICENSED UNDER ACREATIVE COMMONS ATTRIBUTION 3.0UNPORTED LICENSE. 2
  3. 3. DEFINITION OF A BBN A BBN is defined as a pair (G,P) where G and P themselves are defined as followsTHIS W ORK IS LICENSED UNDER ACREATIVE COMMONS ATTRIBUTION 3.0UNPORTED LICENSE. 3
  4. 4. BASIC MATHEMATIC FUNCTIONSTHIS W ORK IS LICENSED UNDER ACREATIVE COMMONS ATTRIBUTION 3.0UNPORTED LICENSE. 4
  5. 5. PROBABILITY DISTRIBUTIONS—MULTINOMIAL AND DIRICHLETTHIS W ORK IS LICENSED UNDER ACREATIVE COMMONS ATTRIBUTION 3.0UNPORTED LICENSE. 5
  6. 6. PROBABILITY DISTRIBUTIONS—DIRICHLET-MULTINOMIALTHIS W ORK IS LICENSED UNDER ACREATIVE COMMONS ATTRIBUTION 3.0UNPORTED LICENSE. 6
  7. 7. PROBABILITY DISTRIBUTION—DIRICHLET-MULTINOMIAL(CONTINUED)THIS W ORK IS LICENSED UNDER ACREATIVE COMMONS ATTRIBUTION 3.0UNPORTED LICENSE. 7
  8. 8. PROBABILITY DISTRIBUTION—DIRICHLET-MULTINOMIAL(CONTINUED)THIS W ORK IS LICENSED UNDER ACREATIVE COMMONS ATTRIBUTION 3.0UNPORTED LICENSE. 8
  9. 9. PROBABILITY DISTRIBUTION—DIRICHLET-MULTINOMIAL(CONTINUED)THIS W ORK IS LICENSED UNDER ACREATIVE COMMONS ATTRIBUTION 3.0UNPORTED LICENSE. 9
  10. 10. BAYES’ THEOREMTHIS W ORK IS LICENSED UNDER ACREATIVE COMMONS ATTRIBUTION 3.0UNPORTED LICENSE. 10
  11. 11. ASSUMPTIONSTHIS W ORK IS LICENSED UNDER ACREATIVE COMMONS ATTRIBUTION 3.0UNPORTED LICENSE. 11
  12. 12. BAYESIAN DIRICHLET (BD) SCORINGFUNCTIONTHIS W ORK IS LICENSED UNDER ACREATIVE COMMONS ATTRIBUTION 3.0UNPORTED LICENSE. 12
  13. 13. SOME DIFFERENT BAYESIAN SCORINGFUNCTIONSTHIS W ORK IS LICENSED UNDER ACREATIVE COMMONS ATTRIBUTION 3.0UNPORTED LICENSE. 13
  14. 14. SOME DIFFERENT BAYESIAN SCORINGFUNCTIONS (CONTINUED)THIS W ORK IS LICENSED UNDER ACREATIVE COMMONS ATTRIBUTION 3.0UNPORTED LICENSE. 14
  15. 15. SUMMARYTHIS W ORK IS LICENSED UNDER ACREATIVE COMMONS ATTRIBUTION 3.0UNPORTED LICENSE. 15

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