Reasoning Pa erns

Probabilis3c   Graphical   Models  

Representa3on   Bayesian  Networks  

Reasoning   Pa1erns   Daphne  Koller  

The Student Network

d0

d1

0.6

0.4

i0 0.7 Difficulty

i0,d0 i0,d1 i1,d0 i1,d1

g1 0.3 0.05 0.9 0.5

g2 0.4 0.25 0.08 0.3

g3 0.3 0.7 0.02 0.2

i1 0.3

Intelligence Grade

SAT

i0 i1

s0 0.95 0.2

s1 0.05 0.8

Letter

g1 g2 g3

l0 0.1 0.4 0.99

l1 0.9 0.6 0.01 Daphne  Koller  

Causal Reasoning Intelligence

Difficulty Grade

SAT

P(l1) ≈ 0.5 P(l1 | i0 ) ≈ 0.39

Letter

P(l1 | i0 , d0) ≈ 0.51 Daphne  Koller  

Evidential Reasoning P(d1) = 0.4 P(d1 | g3) ≈ 0.63

P(i1) = 0.3 P(i1 | g3) ≈0.08

Difficulty Student gets a C  i0,d0 i0,d1 i1,d0 i1,d1

g1 0.3 0.05 0.9 0.5

g2 0.4 0.25 0.08 0.3

g3 0.3 0.7 0.02 0.2

Intelligence Grade

SAT

Letter

Daphne  Koller  

Intercausal Reasoning P(d1) = 0.4 P(d1 | g3) ≈ 0.63 Class is hard!

P(i1) = 0.3 P(i1 | g3) ≈ 0.08 P(i1 | g3, d1) ≈ 0.11

Difficulty

Student gets a C 

Intelligence Grade

SAT

Letter

Daphne  Koller  

Intercausal Reasoning Explained X1

X2 Y

OR

X1

X2

Y  

Prob  

0  

0  

0

0.25

0  

1  

1

0.25

1  

0  

1

0.25

1  

1

1

0.25

Daphne  Koller  

Intercausal Reasoning II P(i1) = 0.3 P(i1 | g2) ≈ 0.175 P(i1 | g2, d1) ≈ 0.34 Difficulty

Intelligence

Class is hard! Student gets a B 

Grade

g2  

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(d1) = 0.4 P(d1 | g3) ≈ 0.63 P(d1 | g3, s1) ≈ 0.76 Difficulty

P(i1) = 0.3 P(i1 | g3) ≈ 0.08 P(i1 | g3, s1) ≈ 0.58 Intelligence

Grade Letter

SAT Student aces the SAT 

Student gets a C  Daphne  Koller