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Graphical Models Representing Probabilistic Features in Log-Linear Models

Explore shared features and templates in log-linear models representing the repetition intelligence and grades of nested students in courses with varying difficulty levels. The model allows for collective inference in overlapping plates by sharing explicit parameters for intelligence, grades, and difficulty, facilitating correlations across multiple students and courses. Learn how the plate dependency model works and how it aids in reusing parameters and structure in a ground network, enhancing the model's expressive power across different languages.

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Graphical Models Representing Probabilistic Features in Log-Linear Models

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  1. Representation Probabilistic Graphical Models Template Models Shared Features in Log-Linear Models

  2. Modeling Repetition

  3. Intelligence I(s1)‏ I(s2)‏ Grade G(s1)‏ G(s2)‏ Students s

  4. Nested Plates Courses c Difficulty Intelligence Grade Students s D(c1)‏ D(c2)‏ I(s1,c1)‏ I(s2,c1)‏ I(s1,c2)‏ I(s2,c2)‏ G(s1,c1)‏ G(s2,c1)‏ G(s1,c1)‏ G(s2,c1)‏

  5. Overlapping Plates Difficulty Intelligence Grade Courses c Students s D(c2)‏ D(c1)‏ I(s1)‏ I(s2)‏ G(s1,c1)‏ G(s1,c2)‏ G(s2,c1)‏ G(s2,c2)‏

  6. Explicit Parameter Sharing D I G D(c2)‏ D(c1)‏ I(s1)‏ I(s2)‏ G(s1,c1)‏ G(s1,c2)‏ G(s2,c1)‏ G(s2,c2)‏

  7. C Welcome to Geo101 Welcome to A low high CS101 Collective Inference easy / hard low / high

  8. Plate Dependency Model • For a template variable A(U1,…,Uk): • Template parents B1(U1),…,Bm(Um) • CPD P(A | B1,…, Bm)

  9. Ground Network • A(U1,…,Uk) with parents B1(U1),…,Bm(Um)

  10. Plate Dependency Model • For a template variable A(U1,…,Uk): • Template parents B1(U1),…,Bm(Um)

  11. Summary • Template for an infinite set of BNs, each induced by a different set of domain objects • Parameters and structure are reused within a BN and across different BNs • Models encode correlations across multiple objects, allowing collective inference • Multiple “languages”, each with different tradeoffs in expressive power

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