Lecture 6

I p gi dp s i p lgp j l s p h g j

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Unformatted text preview: D) D φC (C )φD (D, C ) C I φH (H, G, J ) τ3(G, S ) φL (L, G) φJ (J, L, S ) = C φL (L, G) φ( G, I, D)τ1(D) φS (S, I )φI (I )τ2(G, I ) φH (H, G, J ) H G S = φC (C )φD (D, C )φI (I )φG (G, I, D)φS (S, I )φL(L, G)φJ (J, L, S )φH (H, G, J ) = φC (C )φD (D, C ) C D I H φL (L, G) φJ (J, L, S ) L P (C )P (D|C )P (I )P (G|I, D)P (S |I )P (L|G)P (J |L, S )P (H |G, J ) = φ( G, I, D) D φS (S, I )φI (I ) φH (H, G, J ) φL (L, G) C = φS (S, I )φI (I ) I τ2 (G,I ) P (C, D, I, G, S, L, J, H ) S φH (H, G, J ) H G S = • Key idea 2: use (non-serial) dynamic programming to cache shared subexpressions. L φL (L, G) G φJ (J, L, S ) = • Key idea 1: push sum inside products. P (J ) = S τ1 (D) Letter Happy φJ (J, L, S ) L SAT τ6 (J, L) = L τ7 (J ) Different ordering Dealing with evidence: method 1 Coherence D H C L Difficulty G I S φG (G, I, D)φL(L, )φH (H, G, J ) φI (I )φS (S, I ) φJ (J, L, S ) φD (D, C ) P (J ) = Grade τ1 (I,D,L,J,H ) = φD (D, C ) D C φJ (J, L, S ) H L S φD (D, C ) D C φJ (J, L, S )τ2(D, L, S, J, H ) H L φD (D, C ) D C τ3(D, L, J, H ) H L τ4 (D,J,H ) = φD (D, C ) D C τ4 (D, J, H ) C,D,G,L,S φD (D, C )τ5(D, J ) D • The denominator is P (e) = P (I = 1, H = 0). C τ6 (D,J ) = Job H τ5 (D,J ) = Happy • We can instantiate observed variables to their observed value: P (J, I = 1, H = 0) ∝ P (J, I = 1, H = 0) P (J |I = 1, H = 0) = P (I = 1, H = 0) = P (C, D, I = 1, G, S, L, J, H = 0) S τ3 (D,L,J,H ) = SAT Letter φI (I )φS (S, I )τ1(I, D, L, J, H ) I τ2 (D,L,S,J,H ) = Intelligence • For Markov networks, the denominator is P (e) × Z . τ6 (D, J ) D τ7 (J ) Dealing with evidence: method 2 • We can associate a local evidence potential with every node, and set φi(Xi) = δ (Xi, x∗) if Xi is observed to have value x∗, and i i φi(Xi) = 1 otherwise: P (X1:n|ev ) ∝ P (X1:n) P (evi|Xi) i • e.g., P (J |I = 1, H = 0) ∝ P (C, D, I, G, S, L, J, H )δI (I, 1)δH (H, 0) C,D,I,G,S,L,J,H...
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