Sum Product Algorithm

# the not sum notation hx1 x2 x3 x2 instructor arindam

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## This document was uploaded on 03/18/2014 for the course CS&E 5512 at Minnesota.

Ask a homework question - tutors are online