Computer Science 5541 Artificial Intelligence Homework Assignment 5 (20 points) Due December 16, 2010

1. Page 764, Exercise 18.6 (3rd edition)
2. For the data points from Exercise 18.6 imagine you are using a perceptron with linear activations (the input units are A1, A2, A3 and the special unit that is always 1 and the output is y, there is a weight from each input to the output unit). Set all of the weights initially to 0. Show your work to determine how the weights would change after the first presentation of the data, and then how the weights would change after the second presentation of the data. Assume a learning rate of 0.2.
3. A test for a rare disease is 99% accurate in identifying the disease when the person has the disease and 97% accurate when the person does not have the disease. .5% of the population has the disease. Rich takes the test and it comes up positive (the test indicates he may have the disease). Using Bayes rules, what is the likelihood Rich actually has the disease (hint: the probability that Rich has the disease plus the probability that Rich does not have the disease must add up to 1)? If he takes a second test, and the tests are conditionally independent, how likely is it that he has the disease?