Bayesian scoring functions for Bayesian Belief Networks

May 10, 2013Download as PPTX, PDF1 like1,738 views

This document outlines Bayesian scoring functions that are used to score Bayesian belief networks (BBNs). It defines BBNs and covers the probability distributions and mathematical concepts that Bayesian scoring functions are based on, such as the multinomial and Dirichlet distributions. The document then provides examples of several Bayesian scoring functions, including the Bayesian Dirichlet scoring function, K2 scoring function, and BDe and BDeu scoring functions.

BAYESIAN
SCORING
FUNCTIONS FOR
BAYESIAN BELIEF
NETWORKS (BBNS)
Jee Vang, vangjee@gmail.com
Version 3.1
This work is licensed under a Creative Commons Attribution 3.0
Unported License.

PURPOSE AND OUTLINE
? Purpose: concisely illustrate how some Bayesian scoring
functions have been established to score Bayesian belief
networks (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)
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UNPORTED LICENSE. 2

DEFINITION OF A BBN
? ?
A BBN is defined as a pair (G,P) where G and P themselves are defined as follows
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UNPORTED LICENSE. 3

BASIC MATHEMATIC FUNCTIONS
?
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UNPORTED LICENSE. 4

PROBABILITY DISTRIBUTIONS��
MULTINOMIAL AND DIRICHLET
?
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CREATIVE COMMONS ATTRIBUTION 3.0
UNPORTED LICENSE. 5

PROBABILITY DISTRIBUTIONS��
DIRICHLET-MULTINOMIAL
?
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CREATIVE COMMONS ATTRIBUTION 3.0
UNPORTED LICENSE. 6

PROBABILITY DISTRIBUTION��
DIRICHLET-MULTINOMIAL
(CONTINUED)
?
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UNPORTED LICENSE. 7

PROBABILITY DISTRIBUTION��
DIRICHLET-MULTINOMIAL
(CONTINUED)
?
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UNPORTED LICENSE. 8

PROBABILITY DISTRIBUTION��
DIRICHLET-MULTINOMIAL
(CONTINUED)
?
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CREATIVE COMMONS ATTRIBUTION 3.0
UNPORTED LICENSE. 9

BAYES�� THEOREM
?
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UNPORTED LICENSE. 10

ASSUMPTIONS
?
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BAYESIAN DIRICHLET (BD) SCORING
FUNCTION
?
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SOME DIFFERENT BAYESIAN SCORING
FUNCTIONS
?
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UNPORTED LICENSE. 13

SOME DIFFERENT BAYESIAN SCORING
FUNCTIONS (CONTINUED)
?
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UNPORTED LICENSE. 14

SUMMARY
?
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Bayesian scoring functions for Bayesian Belief Networks

1. BAYESIAN SCORING FUNCTIONS FOR BAYESIAN BELIEF NETWORKS (BBNS) Jee Vang, vangjee@gmail.com Version 3.1 This work is licensed under a Creative Commons Attribution 3.0 Unported License.

2. PURPOSE AND OUTLINE ? Purpose: concisely illustrate how some Bayesian scoring functions have been established to score Bayesian belief networks (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 A CREATIVE COMMONS ATTRIBUTION 3.0 UNPORTED LICENSE. 2

3. DEFINITION OF A BBN ? ? A BBN is defined as a pair (G,P) where G and P themselves are defined as follows THIS W ORK IS LICENSED UNDER A CREATIVE COMMONS ATTRIBUTION 3.0 UNPORTED LICENSE. 3

4. BASIC MATHEMATIC FUNCTIONS ? THIS W ORK IS LICENSED UNDER A CREATIVE COMMONS ATTRIBUTION 3.0 UNPORTED LICENSE. 4

5. PROBABILITY DISTRIBUTIONS�� MULTINOMIAL AND DIRICHLET ? THIS W ORK IS LICENSED UNDER A CREATIVE COMMONS ATTRIBUTION 3.0 UNPORTED LICENSE. 5

6. PROBABILITY DISTRIBUTIONS�� DIRICHLET-MULTINOMIAL ? THIS W ORK IS LICENSED UNDER A CREATIVE COMMONS ATTRIBUTION 3.0 UNPORTED LICENSE. 6

7. PROBABILITY DISTRIBUTION�� DIRICHLET-MULTINOMIAL (CONTINUED) ? THIS W ORK IS LICENSED UNDER A CREATIVE COMMONS ATTRIBUTION 3.0 UNPORTED LICENSE. 7

8. PROBABILITY DISTRIBUTION�� DIRICHLET-MULTINOMIAL (CONTINUED) ? THIS W ORK IS LICENSED UNDER A CREATIVE COMMONS ATTRIBUTION 3.0 UNPORTED LICENSE. 8

9. PROBABILITY DISTRIBUTION�� DIRICHLET-MULTINOMIAL (CONTINUED) ? THIS W ORK IS LICENSED UNDER A CREATIVE COMMONS ATTRIBUTION 3.0 UNPORTED LICENSE. 9

10. BAYES�� THEOREM ? THIS W ORK IS LICENSED UNDER A CREATIVE COMMONS ATTRIBUTION 3.0 UNPORTED LICENSE. 10

11. ASSUMPTIONS ? THIS W ORK IS LICENSED UNDER A CREATIVE COMMONS ATTRIBUTION 3.0 UNPORTED LICENSE. 11

12. BAYESIAN DIRICHLET (BD) SCORING FUNCTION ? THIS W ORK IS LICENSED UNDER A CREATIVE COMMONS ATTRIBUTION 3.0 UNPORTED LICENSE. 12

13. SOME DIFFERENT BAYESIAN SCORING FUNCTIONS ? THIS W ORK IS LICENSED UNDER A CREATIVE COMMONS ATTRIBUTION 3.0 UNPORTED LICENSE. 13

14. SOME DIFFERENT BAYESIAN SCORING FUNCTIONS (CONTINUED) ? THIS W ORK IS LICENSED UNDER A CREATIVE COMMONS ATTRIBUTION 3.0 UNPORTED LICENSE. 14

15. SUMMARY ? THIS W ORK IS LICENSED UNDER A CREATIVE COMMONS ATTRIBUTION 3.0 UNPORTED LICENSE. 15

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Bayesian scoring functions for Bayesian Belief Networks

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Bayesian scoring functions for Bayesian Belief Networks