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Reasoning Patterns

Representation. Probabilistic Graphical Models. Bayesian Networks. Reasoning Patterns. d 0. d 1. i 0. i 1. 0.6. 0.4. 0.7. 0.3. g 1. g 2. g 3. i 0 ,d 0. 0.3. 0.4. 0.3. i 0 ,d 1. 0.05. 0.25. 0.7. s 0. s 1. i 1 ,d 0. 0.9. 0.08. 0.02. i 0. 0.95. 0.05. i 1 ,d 1. 0.5.

jolene-williamson
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Reasoning Patterns

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  1. Representation Probabilistic Graphical Models Bayesian Networks Reasoning Patterns

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

  3. Causal Reasoning Intelligence Intelligence Difficulty Difficulty Grade SAT P(l1) ≈ 0.5 Letter P(l1 | i0) ≈ 0.39 P(l1 | i0 , d0) ≈ 0.51

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

  5. 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

  6. Intercausal Reasoning Explained X1 X2 Y OR

  7. 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 g2 Student gets a B  Letter

  8. 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 

  9. 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 Student gets a C 

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