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Reasoning Patterns Bayesian Networks Representation Probabilistic
Graphical Models Bayesian Networks Reasoning Patterns
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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
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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 ) ≈ 0.39 P(l1 | i0 , d0) ≈ 0.51
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Evidential Reasoning P(d1) = 0.4 P(i1) = 0.3 P(d1 | g3) ≈ P(i1 | g3) ≈
0.63 P(i1 | g3) ≈ 0.08 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
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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
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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
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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
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Intercausal Reasoning Explained
Y Prob 0.25 1 X1 X2 Y OR
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Intercausal Reasoning II
P(i1) = 0.3 P(i1 | g2) ≈ 0.175 P(i1 | g2, d1) ≈ 0.34 Difficulty Difficulty Intelligence Class is hard! Grade SAT Student gets a B g2 Letter 0.175, 0.34
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Student Aces the SAT What happens to the posterior probability that the class is hard? Difficulty Intelligence Grade SAT Student aces the SAT Letter Student gets a C
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Student Aces the SAT What happens to the posterior probability that the class is hard? Difficulty Intelligence Goes up Grade SAT Goes down Student aces the SAT Doesn’t change Letter We can’t know Student gets a C
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Student Aces the SAT P(d1) = 0.4 P(i1) = 0.3 P(d1 | g3) ≈ 0.63
P(i1 | g3) ≈ 0.08 P(d1 | g3, s1) ≈ 0.76 P(i1 | g3, s1) ≈ 0.58 Difficulty Intelligence Grade SAT Student aces the SAT Letter 0.76, 0.58 Student gets a C
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