Daphne Koller Bayesian Networks Semantics & Factorization Probabilistic Graphical Models Representation.

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Presentation transcript:

Daphne Koller Bayesian Networks Semantics & Factorization Probabilistic Graphical Models Representation

Daphne Koller Grade Course Difficulty Student Intelligence Student SAT Reference Letter

Daphne Koller The Student Network IntelligenceDifficulty Grade Letter SAT g2g i 1,d i 0,d g1g1 g3g3 0.2i 1,d 1 0.3i 0,d 0 l1l1 l0l g1g1 0.01g3g3 0.6g2g s0s0 s1s1 0.8i1i1 0.05i0i d1d1 d0d i1i1 i0i0

Template vertLeftWhite2 Defining a joint distribution What is the joint distribution P(D,I,G,S,L)? P(D) P(I) P(G) P(S) P(L) P(D) P(I) P(G|I,D) P(S|I) P(L|G) P(D) P(I) P(G|I) P(G|D) P(S|I) P(L|G) IntelligenceDifficulty Grade Letter SAT P(D|G) P(I|D) P(S|I) P(G|L,I,D) P(L|G)

Daphne Koller The Chain Rule for Bayesian Nets IntelligenceDifficulty Grade Letter SAT

Daphne Koller Bayesian Network A Bayesian network is:

Daphne Koller BN Is a Legal Distribution

Template vertLeft1 What is the value of 1 P(L) P(G) None of the above

Daphne Koller P Factorizes over G Let G be a graph over X 1,…,X n. P factorizes over G if P(X 1,…,X n ) =

Daphne Koller Genetic Inheritance Homer Bart Marge LisaMaggie Clancy Jackie Selma

Daphne Koller BNs for Genetic Inheritance G Homer G Bart G Marge G Lisa G Maggie G Clancy G Jackie G Selma B Clancy B Jackie B Selma B Homer B Marge B Bart B Lisa B Maggie

Daphne Koller END END END

Daphne Koller

The Chain Rule for Bayesian Nets IntelligenceDifficulty Grade Letter SAT g2g i 1,d i 0,d g1g1 g3g3 0.2i 1,d 1 0.3i 0,d 0 l1l1 l0l g1g1 0.01g3g3 0.6g2g s0s0 s1s1 0.8i1i i0i d1d1 d0d i1i1 i0i0 P(D,I,G,S,L) = P(D) P(I) P(G | I,D) P(L | G) P(S | I)

Template vertLeftWhite1 Suppose  is at a local minimum of a function. What will one iteration of gradient descent do? Leave  unchanged. Change  in a random direction. Move  towards the global minimum of J(  ). Decrease .

Template vertLeftWhite1 Consider the weight update: Which of these is a correct vectorized implementation?

Template vertLeftWhite2 Fig. A corresponds to  =0.01, Fig. B to  =0.1, Fig. C to  =1. Fig. A corresponds to  =0.1, Fig. B to  =0.01, Fig. C to  =1. Fig. A corresponds to  =1, Fig. B to  =0.01, Fig. C to  =0.1. Fig. A corresponds to  =1, Fig. B to  =0.1, Fig. C to  =0.01.

Template vertLeftWhite2

Template block2x2White1 Ordering of buttons is: 13 24