Bayesian Networks Variable Elimination Algorithm：贝叶斯网络变量消除算法.ppt

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Bayesian Networks Variable Elimination Algorithm：贝叶斯网络变量消除算法.ppt

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Bayesian Networks Variable Elimination Algorithm：贝叶斯网络变量消除算法

Bayesian NetworksBucket Elimination Algorithm 主講人：虞台文大同大學資工所智慧型多媒體研究室 Content Basic Concept Belief Updating Most Probable Explanation (MPE) Maximum A Posteriori (MAP) Bayesian NetworksBucket Elimination Algorithm Basic Concept 大同大學資工所智慧型多媒體研究室 Satisfiability Resolution Direct Resolution Direct Resolution Direct Resolution Direct Resolution Queries on Bayesian Networks Belief updating Finding the most probable explanation (mpe) Given evidence, finding a maximum probability assignment to the rest of variables. Maximizing a posteriori hypothesis (map) Given evidence, finding an assignment to a subset of hypothesis variables that maximize their probability. Maximizing the expected utility of the problem (meu) Given evidence and utility function, finding a subset of decision variables that maximize the expected utility. Bucket Elimination The algorithm will be used as a framework for various probabilistic inferences on Bayesian Networks. Preliminary – Elimination Functions Preliminary – Elimination Functions Preliminary – Elimination Functions Preliminary – Elimination Functions Bayesian NetworksBucket Elimination Algorithm Belief Updating 大同大學資工所智慧型多媒體研究室 Goal Basic Concept of Variable Elimination Basic Concept of Variable Elimination Basic Concept of Variable Elimination Basic Concept of Variable Elimination Basic Concept of Variable Elimination Basic Concept of Variable Elimination Basic Concept of Variable Elimination Basic Concept of Variable Elimination Basic Concept of Variable Elimination Basic Concept of Variable Elimination Basic Concept of Variable Elimination Bucket Elimination Algorithm Complexity The BuckElim Algorithm can be applied to any ordering. The arity of the function recorded in a bucket the numbers of variables appearing in the processed bucked, excluding the bucket’s variable. Time and Space complexity is exponentially grow with a function of arity r. The arity is dependent on the ordering. How many possible orderings for BN’s varia