BayesianClassification

BayesianClassification - 3/16/11 Bayesian Networks Def: A...

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3/16/11 1 Bayesian Networks Def : A Bayesian belief network is a graph in which – Nodes correspond to random variables – Directed links connect pairs of nodes and indicate a causal link or influence. – Each node has a conditional probability table that quantifies the effects parents of the node have on the node. – The graph is acyclic. Example Bayesian Net family_out hear_bark dog_out light_on has_fleas Pr(fo) = 0.15 Pr(hf) = 0.01 Pr(lo|fo) = 0.60 Pr(lo| ¬ fo) = 0.05 Pr(hb|do) = 0.70 Pr(hb| ¬ do) = 0.01 Pr(do|fo,hf) = 0.99 Pr(do| ¬ fo,hf) = 0.97 Pr(do|fo, ¬ hf) = 0.90 Pr(do| ¬ fo, ¬ hf) = 0.30 Note: Full joint requires 2 5 = 32 values. The net only specifies 10.
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2 Naïve Bayes Algorithm Naïve_Bayes_Learn( examples ) For each target value v j P' ( v j ) estimate P ( v j ) For each attribute value a i of each attribute a P' ( a i | v j ) estimate P ( a i | v j ) Classify_New_Instance( x ) P ( v j ) estimated as proportion of examples labeled v j .
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BayesianClassification - 3/16/11 Bayesian Networks Def: A...

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