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Preliminaries: Independence
Probabilistic Graphical Models Introduction Preliminaries: Independence
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Independence
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Independence P(I,D) I D G Prob. i0 d0 g1 0.126 g2 0.168 g3 d1 0.009
0.045 i1 0.252 0.0224 0.0056 0.06 0.036 0.024 I Prob i0 0.6 i1 0.4 P(I,D) I D Prob i0 d0 0.42 d1 0.18 i1 0.28 0.12 D Prob d0 0.7 d1 0.3
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Conditional Independence
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Conditional Independence
G Prob. i0 d0 g1 0.126 g2 0.168 g3 d1 0.009 0.045 i1 0.252 0.0224 0.0056 0.06 0.036 0.024 P(I,D | g1) I D Prob. i0 d0 0.282 d1 0.02 i1 0.564 0.134
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Conditional Independence
S G Prob. i0 s0 g1 0.126 g2 0.168 g3 s1 0.009 0.045 i1 0.252 0.0224 0.0056 0.06 0.036 0.024 P(S,G | i0) S Prob s0 0.95 s1 0.05 S G Prob. s0 g1 0.19 g2 0.323 g3 0.437 s1 0.01 0.017 0.023 G Prob. g1 0.2 g2 0.34 g3 0.46
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END END END
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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.
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Consider the weight update:
Which of these is a correct vectorized implementation?
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Fig. A corresponds to a=0.01, Fig. B to a=0.1, Fig. C to a=1.
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Factorized Representations
0.5 c1 c0 0.2 0.8 r0 r1 c1 c0 Cloudy 0.9 0.5 s0 s1 0.1 c1 c0 Sprinkler Rain WetGrass 0.3 0.08 0.25 0.4 g2 0.02 0.9 s1,r0 0.7 0.05 s0,r1 0.5 1 g1 g3 0.2 s1,r1 s0,r0 8 independent parameters
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