Graphical' Models' Local'Structure'...
Transcript of Graphical' Models' Local'Structure'...
Daphne Koller
Tabular Representations
0.3 0.08 0.25
0.4 g2
0.02 0.9 i1,d0 0.7 0.05 i0,d1
0.5
0.3 g1 g3
0.2 i1,d1
0.3 i0,d0
Cough
Pneu- monia Flu TB
Bron- chitis
Daphne Koller
General CPD • CPD P(X | Y1, …, Yk) specifies distribution
over X for each assignment y1, …, yk • Can use any function to specify a factor φ(X, Y1, …, Yk) such that
∑x φ(x, y1, …, yk) = 1 for all y1, …, yk
Daphne Koller
Many Models • Deterministic CPDs • Tree-structured CPDs • Logistic CPDs & generalizations • Noisy OR / AND • Linear Gaussians & generalizations
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A
S
L
(0.8,0.2)
(0.9,0.1) (0.4,0.6)
(0.1,0.9)
s1
a0 a1
s0
l1 l0 Letter SAT
Job
Apply
Tree CPD
Daphne Koller
Letter1 Letter2
Job
Choice
Tree CPD C c1 c2
L2
(0.8,0.2) (0.1,0.9)
l1 l0 L1
(0.9,0.1) (0.3,0.7)
l1 l0
Daphne Koller
C c1 c2
L
(0.8,0.2) (0.1,0.9)
l1 l0 L
(0.9,0.1) (0.3,0.7)
l1 l0
Letter1 Letter2
Job
Choice
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$$
Microsoft Troubleshooters
#$of$parameters:$145$to$55$
Thanks to: Eric Horvitz, Microsoft Research
Daphne Koller
Summary • Compact CPD representation that
captures context-specific dependencies • Relevant in multiple applications: – Hardware configuration variables – Medical settings – Dependence on agent’s action – Perceptual ambiguity
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Independence'of'Causal'Influence'
Probabilis4c'Graphical'Models' Local'Structure'
Representa4on'
Daphne Koller
CPCS
# of parameters: 133,931,430 to 8254
M. Pradhan G. Provan B. Middleton M. Henrion UAI 1994