Probabilistic Graphical Models Acting Decision Making Value of

Probabilistic Graphical Models Acting Decision Making Value of Perfect Information Daphne Koller

Value of Information • VPI(A | X) is the value of observing X before choosing an action at A • D = original influence diagram • DX A = influence diagram with edge X A Daphne Koller

Finding MEU Decision Rules Market Survey Found U Daphne Koller

Value of Information • Theorem: – VPI(A | X) 0 – VPI(A | X) = 0 if and only if the optimal decision rule for D is still optimal for DX A Daphne Koller

Value of Information Example s 1 s 2 s 3 0. 1 0. 2 0. 7 f 0 s 1 s 2 s 3 f 1 0. 9 0. 1 0. 6 0. 4 0. 1 0. 9 State 1 State 2 s 1 s 2 s 3 0. 4 0. 5 0. 1 Funding 1 Company Funding 2 V *(C | S 2) = P(c 2)=1 if S 2 = s 3 P(c 1)=1 otherwise EU(D[c 1]) = 0. 72 EU(D[c 2]) = 0. 33 MEU(DS 1 C) = 0. 743 Daphne Koller

Value of Information Example s 1 s 2 s 3 0. 5 0. 3 0. 2 f 0 s 1 s 2 s 3 f 1 0. 9 0. 1 0. 6 0. 4 0. 1 0. 9 State 1 State 2 s 1 s 2 s 3 0. 4 0. 5 0. 1 Funding 1 Company Funding 2 V *(C | S 2) = P(c 2)=1 if S 2 = s 2, s 3 P(c 1)=1 otherwise EU(D[c 1]) = 0. 35 EU(D[c 2]) = 0. 33 MEU(DS 1 C) = 0. 43 Daphne Koller

Value of Information Example s 1 s 2 s 3 0. 5 0. 3 0. 2 State 1 State 2 s 1 s 2 s 3 0. 4 0. 5 0. 1 f 0 f 1 Funding 1 Company Funding 2 s 1 0. 3 0. 7 s 2 0. 8 s 3 0. 01 0. 99 V *(C | S 2) = P(c 2)=1 if S 2 = s 2, s 3 P(c 1)=1 otherwise EU(D[c 1]) = 0. 788 EU(D[c 2]) = 0. 779 MEU(DS 1 C) = 0. 8142 Daphne Koller

Summary • Influence diagrams provide clear and coherent semantics for the value of making an observation – Difference between values of two IDs • Information is valuable if and only if it induces a change in action in at least one context Daphne Koller

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