FOIL’s information gain.

Consider a training set that contains 100 positive examples and 400 negative
examples. For each of the following candidate rules,
R1: A ?? + (covers 4 positive and 1 negative examples),
R2: B ?? + (covers 30 positive and 10 negative examples),
R3: C ?? + (covers 100 positive and 90 negative examples),
determine which is the best and worst candidate rule according to:

Assume the initial rule is ? ?? +. This rule covers p0 = 100 positive
examples and n0 = 400 negative examples.
The rule R1 covers p1 = 4 positive examples and n1 = 1 negative
example. Therefore, the FOIL’s information gain for this rule is

The rule R2 covers p1 = 30 positive examples and n1 = 10 negative
example. Therefore, the FOIL’s information gain for this rule is

The rule R3 covers p1 = 100 positive examples and n1 = 90 negative
example. Therefore, the FOIL’s information gain for this rule is

Therefore, R3 is the best candidate and R1 is the worst candidate ac-
cording to FOIL’s information gain.