Probabilistic Graphical Models Representation Bayesian Networks Reasoning Patterns









- Slides: 9

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
Probabilistic Graphical Models Representation Bayesian Networks Probabilistic Influence
Probabilistic Graphical Models Representation Bayesian Networks Semantics Factorization
Probabilistic Graphical Models Representation Bayesian Networks Application Diagnosis
Probabilistic Graphical Models Representation Template Models Plate Models
Bayesian Networks Bayesian networks A simple graphical notation
Probabilistic Graphical Models Representation Local Structure LogLinear Models
Probabilistic Graphical Models Representation Markov Networks Conditional Random
Probabilistic Graphical Models Representation Markov Networks General Gibbs
Reasoning with Bayesian Networks Overview Bayesian Belief Networks