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

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

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

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

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

Implications

END END END

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)

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.

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

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