Value of Perfect Information

1. Acting Probabilistic Graphical Models Decision Making Value of Perfect Information

2. 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

3. U Finding MEU Decision Rules Market Survey Found

4. 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

5. V Value of Information Example State1 State2 s3 s3 s1 s1 s2 s2 0.7 0.1 0.4 0.1 0.2 0.5 f1 f0 Funding1 Funding2 0.1 s1 0.9 Company 0.4 s2 0.6 0.9 s3 0.1 P(c2)=1 if S2 = s3 P(c1)=1 otherwise *(C | S2) = EU(D[c1]) = 0.72 EU(D[c2]) = 0.33 MEU(DS1 C) = 0.743

6. V Value of Information Example State1 State2 s3 s3 s1 s1 s2 s2 0.2 0.1 0.4 0.5 0.3 0.5 f1 f0 Funding1 Funding2 0.1 s1 0.9 Company 0.4 s2 0.6 0.9 s3 0.1 P(c2)=1 if S2 = s2,s3 P(c1)=1 otherwise *(C | S2) = EU(D[c1]) = 0.35 EU(D[c2]) = 0.33 MEU(DS1 C) = 0.43

7. V Value of Information Example State1 State2 s3 s3 s1 s1 s2 s2 0.2 0.1 0.4 0.5 0.3 0.5 f1 f0 Funding1 Funding2 0.7 s1 0.3 Company 0.8 s2 0.2 0.99 s3 0.01 P(c2)=1 if S2 = s2,s3 P(c1)=1 otherwise *(C | S2) = EU(D[c1]) = 0.788 EU(D[c2]) = 0.779 MEU(DS1 C) = 0.8142

8. 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

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