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Overview of Probabilistic Graphical Models: Local Structures and Context-Specific Independences

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Explore the fundamentals of Probabilistic Graphical Models (PGMs) focused on local structures. This overview discusses various types of Conditional Probability Distributions (CPDs), including deterministic and context-specific CPDs, and their applications in graphical representation. Delve into specific models like logistic CPDs, noisy OR, and linear Gaussian models. Additionally, examine general factors such as log-linear models and their implications for context-specific independence, particularly how dependencies among variables are structured in relation to deterministic operations.

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Overview of Probabilistic Graphical Models: Local Structures and Context-Specific Independences

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  1. Representation Probabilistic Graphical Models Local Structure Overview

  2. g1 g2 g3 i0,d0 0.3 0.4 0.3 i0,d1 0.05 0.25 0.7 i1,d0 0.9 0.08 0.02 i1,d1 0.5 0.3 0.2 Tabular Representations

  3. General CPD

  4. Many Models • Deterministic CPDs • Context-specific CPDs (trees, rules) • Logistic CPDs & generalizations • Noisy OR / AND • Linear Gaussians & generalizations

  5. General Factors: Log-linear Model

  6. Context-Specific Independence

  7. 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

  8. END END END

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