# Probabilistic Graphical Models Representation Template Models Plate Models

• Slides: 11

Probabilistic Graphical Models Representation Template Models Plate Models Daphne Koller

Modeling Repetition Daphne Koller

Intelligence I(s 1) I(s 2) Grade G(s 1) G(s 2) Students s Daphne Koller

Nested Plates Difficulty Intelligence Grade D(c 1) I(s 1, c 1) G(s 1, c 1) Courses c Students s D(c 2) I(s 2, c 1) G(s 2, c 1) I(s 1, c 2) G(s 1, c 1) I(s 2, c 2) G(s 2, c 1) Daphne Koller

Overlapping Plates Difficulty Courses c Intelligence Grade D(c 2) D(c 1) G(s 1, c 1) Students s I(s 1) G(s 1, c 2) G(s 2, c 1) I(s 2) G(s 2, c 2) Daphne Koller

Explicit Parameter Sharing D D(c 2) D(c 1) G(s 1, c 1) G G(s 1, c 2) I I(s 1) G(s 2, c 1) I(s 2) G(s 2, c 2) Daphne Koller

Collective Inference Welcome to CS 101 C Welcome to Geo 101 easy / hard A low high low / high Daphne Koller

Plate Dependency Model • For a template variable A(U 1, …, Uk): – Template parents B 1(U 1), …, Bm(Um) – CPD P(A | B 1, …, Bm) Daphne Koller

Ground Network • A(U 1, …, Uk) with parents B 1(U 1), …, Bm(Um) Daphne Koller

Plate Dependency Model • For a template variable A(U 1, …, Uk): – Template parents B 1(U 1), …, Bm(Um) Daphne Koller

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 Daphne Koller