Amy and Barbara are separately researching the question of what very rich people like to drink. They are both working from the same data set. An instance in this data set is a person. There are three attributes:
Barbara divides the beverages into two categories: champagne and everything else. She applied Naive Bayes in the same way. The results of her calculation is that, given that a person owns a BMW and a yacht, the probability is more than 90 per cent that his/her favorite drink is champagne.
Describe a data set that supports both of these conclusions. (The kind of "description" you're looking for would be something like, "There are 100 instances of people who own a BMW, own a yacht and drink champagne; 3 instances of people who don't own a BMW, own a yacht, and drink beer;" etc.)
P | Q | R | C | Number of instances. |
---|---|---|---|---|
Y | Y | 1 | N | 20 |
Y | Y | 2 | Y | 1 |
Y | Y | 3 | Y | 2 |
Y | N | 1 | Y | 8 |
Y | N | 2 | Y | 2 |
Y | N | 3 | Y | 0 |
N | Y | 1 | N | 12 |
N | Y | 2 | Y | 2 |
N | Y | 3 | Y | 1 |
N | N | 1 | Y | 25 |
N | N | 2 | Y | 1 |
N | N | 3 | Y | 4 |
Trace the execution of the ID3 algorithm, and show the decision tree that it outputs. At each stage, you should compute the average entropy AVG\_ENTROPY(A,C,T) for each attribute A. (The book calls this "Remainder(A)" (p. 660).)