1. I-equivalence Bayesian Networks Representation Probabilistic Graphical
Models
Bayesian Networks
I-equivalence

2. Different G’s might encode the same independencies
Draw student network

3. Which of the following graphs does not encode the
same independencies as the others? X Y Z X Y Z X Y Z X Y Z

4. I-equivalence
Definition: Two graphs G1 and G2 over X1,…,Xn are I-equivalent if
Chain rule, CPDs

5. Characterizing I-equivalence
Theorem: G1 and G2 are I-equivalent if and only if they have

6. Implications

7. END END END

13. The Chain Rule for Bayesian Nets
Intelligence
Difficulty
Grade
Letter
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 l1 l0
0.99
0.1
0.01
0.6
0.95 s0 s1
0.8 i1 i0 d1 d0
P(D,I,G,S,L) =
P(D) P(I) P(G | I,D) P(L | G) P(S | I)

14. 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.

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

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