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

2. 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

3. 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) ~

4. 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

5. 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

6. 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

7. 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

9. 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

10. 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

11. END

17. Suppose q is at a local minimum of a function
Suppose q is at a local minimum of a function. What will one iteration of gradient descent do?
Leave q unchanged.
Change q in a random direction.
Move q towards the global minimum of J(q).
Decrease q.

18. Consider the weight update:
Which of these is a correct vectorized implementation?

19. Fig. A corresponds to a=0.01, Fig. B to a=0.1, Fig. C to a=1.