Probabilistic Graphical Models Representation Template Models Plate Models
Probabilistic Graphical Models Representation Template Models Plate Models Daphne Koller
Modeling Repetition Outcome Tosses t Outcome(t 1) . . . Outcome(tk) {t 1, …, tk} 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 Let A(U 1, …, Uk) with parents B 1(U 1), …, Bm(Um) • for any instantiation u 1, …, uk to U 1, …, Uk we would have: Daphne Koller
Plate Dependency Model Let A(U 1, …, Uk) with parents B 1(U 1), …, Bm(Um) • For each i, we must have Ui U 1, …, Uk – No indices in parent that are not in child 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
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