# Methods for Analyzing Decision Problems

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```							Methods for Analyzing Decision Problems

Value of information

Aleksandr Tkatsenko

20.05.2009
Outline
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Value of information

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Example

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Information scenarios, utility value function

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Non-utility value functions

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Handling many tests
Value of information
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Decision types:
–   action decisions – change state of other variables
–   test decision – look for more evidence (\$\$)
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Model:
–   only one utility function U
–   one action decision D
–   1..n tests
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Related questions:
–   which test to perform, if any?
–   in what order?
–   is the test worth its price?
Example: Test for Infected Milk?
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Hypothesis variable: Inf = {yes, no}
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Test:
–   cost: 0.06\$
–   P(Test = pos | Inf = no) = P(Test = neg | Inf = yes) = 0.001
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P(Inf = yes) = 0,0007
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Utility:
–   U(D = pour, Inf = no) = 100\$
–   U(D = pour, Inf = yes) = 0\$
–   U(D = discard, Inf = no) = U(D = discard, Inf = yes) = 98\$
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Value function:

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Performing test T which yields t:

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Expected value of performing test T with cost C:

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Expected benefit:

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Expected profit:
Non-utility value functions
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Entropy:

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Variance:

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Convex functions:
–   expected benefit of performing a test is never negative
Handling many tests
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Need to examine all possible sequences of tests → intractable
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Myopic approach: choose repeatedly a test with the highest
positive expected profit
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Effective computation:
–   propagate the states of H to each test node Ti.
–   Apply Bayes' rule:
Many tests with junction trees

if MEU1 – MEU2 > Cost(C) → don't observe C

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