Probabilistic Graphical Models Representation Template Models Plate Models

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Probabilistic Graphical Models Representation Template Models Plate Models Daphne Koller

Probabilistic Graphical Models Representation Template Models Plate Models Daphne Koller

Modeling Repetition Daphne Koller

Modeling Repetition Daphne Koller

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

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

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

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

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

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)

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

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

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