Daphne Koller Variable Elimination Variable Elimination Algorithm Probabilistic Graphical Models Inference.

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Presentation transcript:

Daphne Koller Variable Elimination Variable Elimination Algorithm Probabilistic Graphical Models Inference

Daphne Koller Elimination in Chains ABC E D X

Daphne Koller Elimination in Chains ABC E D X X

Daphne Koller C D I SG L J H D Variable Elimination Goal: P(J) Eliminate: C,D,I,H,G,S,L Compute

Daphne Koller Variable Elimination Goal: P(J) Eliminate: D,I,H,G,S,L C D I SG L J H D Compute

Daphne Koller Variable Elimination Goal: P(J) Eliminate: I,H,G,S,L C D I SG L J H D Compute

Daphne Koller Variable Elimination Goal: P(J) Eliminate: H,G,S,L C D I SG L J H D Compute

Daphne Koller Variable Elimination Goal: P(J) Eliminate: G,S,L C D I SG L J H D Compute

Daphne Koller Variable Elimination Goal: P(J) Eliminate: S,L C D I SG L J H D

Daphne Koller C D I SG L J H D Variable Elimination with evidence Goal: P(J,I=i,H=h) Eliminate: C,D,G,S,L How do we get P(J | I=i,H=h)?

Daphne Koller Variable Elimination in MNs BD C A Goal: P(D) Eliminate: A,B,C At the end of elimination get  3 (D)

Daphne Koller Eliminate-Var Z from 

Daphne Koller VE Algorithm Summary Reduce all factors by evidence – Get a set of factors  For each non-query variable Z – Eliminate-Var Z from  Multiply all remaining factors Renormalize to get distribution

Daphne Koller Summary Simple algorithm Works for both BNs and MNs Factor product and summation steps can be done in any order, subject to: – when Z is eliminated, all factors involving Z have been multiplied in