Probabilistic Graphical Models Representation Bayesian Networks Iequivalence Daphne

Probabilistic Graphical Models Representation Bayesian Networks I-equivalence Daphne Koller

Different G’s might encode the same independencies Daphne Koller

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

I-equivalence Definition: Two graphs G 1 and G 2 over X 1, …, Xn are I-equivalent if Daphne Koller

G Which of the following graphs is I -equivalent to G, shown on right? B C D D A B C D A A B A None of the above

Characterizing I-equivalence Theorem: G 1 and G 2 are I-equivalent if and only if they have Daphne Koller

Implications Daphne Koller

END END Daphne Koller

Daphne Koller

Daphne Koller

Daphne Koller

Daphne Koller

Daphne Koller

The Chain Rule for Bayesian Nets d 0 d 1 i 0 i 1 0. 6 0. 4 0. 7 0. 3 Difficulty i 0, d 0 i 0, d 1 i 1, d 0 i 1, d 1 g 1 0. 3 0. 05 0. 9 0. 5 g 2 0. 4 0. 25 0. 08 0. 3 g 3 0. 7 0. 02 0. 2 Intelligence Grade Letter g 1 g 2 g 3 l 0 0. 1 0. 4 0. 99 P(D, I, G, S, L) = P(D) P(I) P(G | I, D) P(L | G) P(S | I) l 1 0. 9 0. 6 0. 01 SAT i 0 i 1 s 0 s 1 0. 95 0. 2 0. 05 0. 8 Daphne Koller

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. Fig. A corresponds to a=0. 1, Fig. B to a=0. 01, Fig. C to a=1. Fig. A corresponds to a=1, Fig. B to a=0. 01, Fig. C to a=0. 1. Fig. A corresponds to a=1, Fig. B to a=0. 1, Fig. C to a=0. 01.