Probabilistic Graphical Models Representation Template Models Plate Models

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