Sum Product Algorithm

the not sum notation hx1 x2 x3 x2 instructor arindam

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Unformatted text preview: ctions (Contd.) The “not-sum” notation h(x1 , x2 , x3 ) = ∼x2 Instructor: Arindam Banerjee h(x1 , x2 , x3 ) x1 ,x3 The Sum-Product Algorithm Marginalize Product of Functions (Contd.) The “not-sum” notation h(x1 , x2 , x3 ) = ∼x2 h(x1 , x2 , x3 ) x1 ,x3 Recall g (x1 , x2 , x3 , x4 , x5 ) = fA (x1 )fB (x2 )fC (x1 , x2 , x3 )fD (x3 , x4 )fE (x3 , x5 ) Instructor: Arindam Banerjee The Sum-Product Algorithm Marginalize Product of Functions (Contd.) The “not-sum” notation h(x1 , x2 , x3 ) = ∼x2 h(x1 , x2 , x3 ) x1 ,x3 Recall g (x1 , x2 , x3 , x4 , x5 ) = fA (x1 )fB (x2 )fC (x1 , x2 , x3 )fD (x3 , x4 )fE (x3 , x5 ) Computing marginal function using not-sum notations g (x1 , x2 , x3 , x4 , x5 ) gi (xi ) = ∼xi Instructor: Arindam Banerjee The Sum-Product Algorithm MPF using Distributive Law We focus on two examples: g1 (x1 ) and g3 (x3 ) Instructor: Arindam Banerjee The Sum-Product Algorithm MPF using Distributive Law We focus on two examples: g1 (x1 ) and g3 (x3 ) From distributive law g1 (x1 ) = fA (x1 ) fB (x2 )fC (x1 , x2 , x3 ) ∼x1 Instructor: Arindam Banerjee fD (x3 , x4 ) ∼x3 The Sum-Product Algorithm fE (x3 , x5 ) ∼x3 MPF using Distributive Law We focus on two examples: g1 (x1 ) and g3 (x3 ) From distributive law g1 (x1 ) = fA (x1 ) fB (x2 )fC (x1 , x2 , x3 ) ∼x1 fD (x3 , x4 ) ∼x3 fE (x3 , x5 ) ∼x3 Also g3 (x3 ) fA (x1 )fB (x2 )fC (x1 , x2 , x3 ) = fD (x3 , x4 ) ∼x3 ∼x3 Instructor: Arindam Banerjee The Sum-Product Algorithm fE (x3 , x5 ) ∼x3 Message Passing Example: Computing g1 (x1 ) Instructor: Arindam Banerjee The Sum-Product Algorithm Message Passing Example: Computing g2 (x2 ) Instructor: Arindam Banerjee The Sum-Product Algorithm Local Transformation for Message Passing Instructor: Arindam Banerjee The Sum-Product Algorithm Sum-Product Algorithm The overall strategy is simple message passing Instructor: Arindam Banerjee The Sum-Product Algorithm Sum-Product Algorithm The overall strategy is simple message passing To compute gi (xi ), form a rooted tree at xi Instructor: Arindam Banerjee The Sum-Product Algorithm Sum-Product Algorithm The overall strategy is simple message passing To compute gi (xi ), form a rooted tree at xi Apply the following two rules: Instructor: Arindam Banerjee The Sum-Product Algorithm Sum-Product Algorithm The overall strategy is simple message passing To compute gi (xi ), form a rooted tree at xi Apply the following two rules: Product Rule: Instructor: Arindam Banerjee The...
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This document was uploaded on 03/18/2014 for the course CS&E 5512 at Minnesota.

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