Representation Probabilistic Graphical Models Local Structure Overview.

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Presentation transcript:

Representation Probabilistic Graphical Models Local Structure Overview

Tabular Representations 0.3 0.08 0.25 0.4 g2 0.02 0.9 i1,d0 0.7 0.05 i0,d1 0.5 g1 g3 0.2 i1,d1 i0,d0 Pneu- monia Flu TB Bron- chitis Cough k parents, 2^k params

General CPD CPD P(X | Y1, …, Yk) specifies distribution over X for each assignment y1, …, yk Can use any function to specify a factor (X, Y1, …, Yk) such that ∑x (x, y1, …, yk) = 1 for all y1, …, yk

Many Models Deterministic CPDs Tree-structured CPDs Logistic CPDs & generalizations Noisy OR / AND Linear Gaussians & generalizations

Context-Specific Independence Example: OR, AND

Y1 Y2 Which of the following context-specific independences hold when X is a deterministic OR of Y1 and Y2? (Mark all that apply.) X