Probabilistic Graphical Models Representation Bayesian Networks Reasoning Patterns

Probabilistic Graphical Models Representation Bayesian Networks Reasoning Patterns Daphne Koller

The Student Network d 0 d 1 0. 6 0. 4 i 0 0. 7 Difficulty i 0, d 0 i 0, d 1 i 1, d 0 i 1, d 1 g 1 0. 3 0. 05 0. 9 0. 5 g 2 0. 4 0. 25 0. 08 0. 3 g 3 0. 7 0. 02 0. 2 i 1 0. 3 Intelligence Grade SAT i 0 i 1 s 0 0. 95 0. 2 s 1 0. 05 0. 8 Letter g 1 g 2 g 3 l 0 0. 1 0. 4 0. 99 l 1 0. 9 0. 6 0. 01 Daphne Koller

Causal Reasoning Intelligence Difficulty Grade SAT P(l 1) ≈ 0. 5 P(l 1 | i 0 ) ≈ 0. 39 Letter P(l 1 | i 0 , d 0) ≈ 0. 51 Daphne Koller

Evidential Reasoning P(d 1) = 0. 4 P(d 1 | g 3) ≈ 0. 63 P(i 1) = 0. 3 P(i 1 | g 3) ≈0. 08 Difficulty Student gets a C i 0, d 0 i 0, d 1 i 1, d 0 i 1, d 1 g 1 0. 3 0. 05 0. 9 0. 5 g 2 0. 4 0. 25 0. 08 0. 3 g 3 0. 7 0. 02 0. 2 Intelligence Grade SAT Letter Daphne Koller

Intercausal Reasoning P(d 1) = 0. 4 P(d 1 | g 3) ≈ 0. 63 Class is hard! P(i 1) = 0. 3 P(i 1 | g 3) ≈ 0. 08 P(i 1 | g 3, d 1) ≈ 0. 11 Difficulty Student gets a C Intelligence Grade SAT Letter Daphne Koller

Intercausal Reasoning Explained X 1 X 2 Y OR X 1 X 2 Y Prob 0 0. 25 0 1 1 0. 25 1 1 1 0. 25 Daphne Koller

Intercausal Reasoning II P(i 1) = 0. 3 P(i 1 | g 2) ≈ 0. 175 P(i 1 | g 2, d 1) ≈ 0. 34 Difficulty Intelligence Class is hard! Student gets a B Grade g 2 SAT Letter Daphne Koller

Student Aces the SAT • What happens to the posterior probability that the class is hard? Difficulty Intelligence Grade Letter SAT Student aces the SAT Student gets a C Daphne Koller

Student Aces the SAT P(d 1) = 0. 4 P(d 1 | g 3) ≈ 0. 63 P(d 1 | g 3, s 1) ≈ 0. 76 Difficulty P(i 1) = 0. 3 P(i 1 | g 3) ≈ 0. 08 P(i 1 | g 3, s 1) ≈ 0. 58 Intelligence Grade Letter SAT Student aces the SAT Student gets a C Daphne Koller