Lab: Decision Networks and Value of Information

CSC 261 - Artificial Intelligence - Weinman



Summary:
You will investigate using the value of perfect information and expected utility to make a decision. (Adapted from AIMA Exercise 16.17.)

Background

A used car buyer can decide to carry out various tests with various costs (e.g., kick the tires or take the car to a mechanic). Depending on the outcome of these tests, they may decide which car to buy.
Assume you are deciding to whether to buy one particular car but have time to carry out at most one test at a cost of $50. The car could be in good shape or not, and the test might help indicate what shape the car is in. The cost is $1500 and its market value is $2000, but only if it is in good shape. If not, it will take $700 in repairs to get it in good shape.
Your current belief is a 70% chance the car is in good shape. In addition, there is an 80% chance the car will pass the test if it is in good shape, but a 35% it will pass the test if it is in bad shape.

Goal

In helping us decide whether to buy the car, we are trying to assess the value of the test outcome - what would we be willing to pay for the test? That is, we want to know its value to us. Thus, the actual cost of the test does not factor into any of the calculations below.

Exercises

  1. What are the decision variables (nodes) for this problem?
  2. What are the chance variables (nodes) for this problem?
  3. Draw the decision network for this problem, connecting the utility node only to the variables that affect utility.
  4. Calculate the expected utility (i.e., net gain) of buying the car with no test results.
  5. Given the information in the background above, what is the (marginal) probability that the car will pass the test?
  6. Using your calculation above, what is the probability the car is in good shape given it passes the test?
  7. What is the probability the car is in good shape given it fails the test?
  8. What is the expected utility of buying the car given a passed test? Given a failed test?
    Note: Do NOT include the cost of the test. We're trying to find the test's value to us, not its cost.
  9. With the information in the background, what is the expected utility of not buying the car given passed or failed test?
    (Once again, we ignore the cost of the test.)
  10. What is the optimal decision in each situation?
  11. What do you sense the value of the performing the test is?
  12. Calculate the value of information of the test.
  13. Derive an optimal conditional plan for the buyer.
Copyright © 2011, 2013, 2015, 2018 Jerod Weinman.
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