class_11_19 - Statistical Data Mining ORIE 474 Fall 2007...

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Statistical Data Mining ORIE 474 Fall 2007 Tatiyana V. Apanasovich 11/19/07 Bayesian NN
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Why the Excitement? What are they? Bayesian nets are a network-based framework for representing and analyzing models involving uncertainty Where did they come from? Cross fertilization of ideas between the artificial intelligence, decision analysis, and statistic communities Why the sudden interest? Development of propagation algorithms followed by availability of easy to use commercial software Growing number of creative applications How are they different from other knowledge representation and probabilistic analysis tools? Different from other knowledge-based systems tools because uncertainty is handled in mathematically rigorous yet efficient and simple way Different from other probabilistic analysis tools because of network representation of problems, use of Bayesian statistics, and the synergy between these
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Definition of a Bayesian Network Factored joint probability distribution as a directed graph: structure for representing knowledge about uncertain variables computational architecture for computing the impact of evidence on beliefs Knowledge structure: variables are depicted as nodes arcs represent probabilistic dependence between variables conditional probabilities encode the strength of the dependencies Computational architecture: computes posterior probabilities given evidence about selected nodes exploits probabilistic independence for efficient computation
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Joint Probability Distribution(JPD) P(A, B) JPD, Probability of both A and B. P(A,B)<P(A|B) P(A|B) Conditional probability. The probability of A, given that B already happen. A B
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Bayes Rule Based on definition of conditional probability p(A i |E) is posterior probability given evidence E p(A i ) is the prior probability P(E|A i ) is the likelihood of the evidence given A i p(E) is the preposterior probability of the evidence = = = = i i i i i i i i ) )p(A A | p(E ) )p(A A | p(E p(E) ) )p(A A | p(E E) | p(A p(B) A)p(A) | p(B p(B) B) p(A, B) | p(A A 1 A 2 A 3 A 4 A 5 A 6 E
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Joint Distributions A1 A0 B1 B0 B1 B0 C1 0.00175 0.00175 0.009975 0.009975 C0 0.00075 0.00075 0.987525 0.987525 3 variables A, B, C need a table of 8 values.
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