Reasoning Patterns Bayesian Networks Representation Probabilistic

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Presentation transcript:

Reasoning Patterns Bayesian Networks Representation Probabilistic Graphical Models Bayesian Networks Reasoning Patterns

The Student Network 0.4 0.6 d1 d0 0.3 0.7 i1 i0 Difficulty Intelligence 0.2 0.95 s0 s1 0.8 i1 0.05 i0 0.3 0.08 0.25 0.4 g2 0.02 0.9 i1,d0 0.7 0.05 i0,d1 0.5 g1 g3 0.2 i1,d1 i0,d0 Grade SAT Letter l1 l0 0.99 0.4 0.1 0.9 g1 0.01 g3 0.6 g2

Causal Reasoning P(l1) ~ 0.5 P(l1 | i0 ) ~ P(l1 | i0 , d0) ~ Difficulty Difficulty Intelligence Intelligence Grade SAT P(l1) ~ 0.5 Letter P(l1 | i0 ) ~ P(l1 | i0 , d0) ~

Evidential Reasoning P(d1) = 0.4 P(i1) = 0.3 P(d1 | g3) ≈ P(i1 | g3) ≈ Difficulty Intelligence Student gets a C  Grade SAT 0.3 0.08 0.25 0.4 g2 0.02 0.9 i1,d0 0.7 0.05 i0,d1 0.5 g1 g3 0.2 i1,d1 i0,d0 Letter 0.63, 0.08

We find out that class is hard What happens to the posterior probability of high intelligence? Intelligence Difficulty Grade Letter SAT Class is hard! Student gets a C  Goes up Goes down Doesn’t change We can’t know

Intercausal Reasoning P(d1) = 0.4 P(i1) = 0.3 P(d1 | g3) ≈ 0.63 P(i1 | g3) ≈ 0.08 P(i1 | g3, d1) ≈ 0.11 Difficulty Intelligence Class is hard! Grade SAT Student gets a C  Letter 0.11

Intercausal Reasoning II P(i1) = 0.3 P(i1 | g2) ≈ P(i1 | g2, d1) ≈ Difficulty Difficulty Intelligence Class is hard! Grade SAT Student gets a B  Letter 0.175, 0.34

Student Aces the SAT What happens to the posterior probability that the class is hard? Intelligence Difficulty Grade Letter SAT Student gets a C  Goes up Goes down Doesn’t change Student aces the SAT  We can’t know

Multiple Evidence P(d1) = 0.4 P(i1) = 0.3 P(d1 | g3) ≈ 0.63 P(i1 | g3) ≈ 0.08 P(d1 | g3, s1) ≈ P(i1 | g3, s1) ≈ Difficulty Intelligence Grade SAT Student gets a C  Student aces the SAT  Letter 0.76, 0.58

END

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