The likelihood ratio statistic.
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:
For R1, the expected frequency for the positive class is 5×100/500 = 1
and the expected frequency for the negative class is 5 × 400/500 = 4.
Therefore, the likelihood ratio for R1 is
For R2, the expected frequency for the positive class is 40×100/500 = 8
and the expected frequency for the negative class is 40 × 400/500 = 32.
Therefore, the likelihood ratio for R2 is
For R3, the expected frequency for the positive class is 190×100/500 =
38 and the expected frequency for the negative class is 190×400/500 =
152. Therefore, the likelihood ratio for R3 is
Therefore,
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