Lift

Lift is a measure of the relative utility of a classification rule. It is calculated by dividing the probability of the consequent of the rule, given its antecedent by the prior probability of the consequent:

$$\displaystyle\begin{array}{rcl} \mathrm{lift}(x \rightarrow y) = P(Y = y\vert X = x)/P(Y = y).& & {}\\ \end{array}$$

In practice, the probabilities are usually estimated from either training data or test data. In this case,

$$\displaystyle\begin{array}{rcl} \mathrm{lift}(x \rightarrow y) = F(Y = y\vert X = x)/F(Y = y).& & {}\\ \end{array}$$

where F(Y = y | X = x) is the frequency with which the consequent occurs in the data in the context of the antecedent and F(Y = y) is the frequency of the consequent in the data.