1. Daphne Koller Template Models Plate Models Probabilistic Graphical Models Representation

2. Daphne Koller Modeling Repetition

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

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

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

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

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

8. Daphne Koller Plate Dependency Model For a template variable A(U 1,…,U k ): – Template parents B 1 (U 1 ),…,B m (U m ) – CPD P(A | B 1,…, B m )

9. Daphne Koller Ground Network A(U 1,…,U k ) with parents B 1 (U 1 ),…,B m (U m )

10. Daphne Koller Plate Dependency Model For a template variable A(U 1,…,U k ): – Template parents B 1 (U 1 ),…, B m (U m )

11. Template block2x2-1 Ordering of buttons is: 13 24 Which of the following plate models could have induced the ground network shown on the right? A(x 1 ) ‏ C(x 1,y 1 ) ‏ B(x 1 ) ‏ C(x 1,y 2 ) ‏ D(x 1,z 1 ) ‏ E(x 1,y 1,z 1 ) ‏ E(x 1,y 2,z 1 ) ‏ A‏A‏ C‏C‏ B‏B‏ D‏D‏ E‏E‏ x y z A‏A‏ C‏C‏ B‏B‏ D‏D‏ E‏E‏ x y z A‏A‏ C‏C‏ B‏B‏ D‏D‏ E‏E‏ x y z A‏A‏ C‏C‏ B‏B‏ D‏D‏ E‏E‏ x y z

12. 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