Editing Association rule learning (section)

=== Lift ===
The ''[[lift (data mining)|lift]]'' of a rule is defined as:

<math> \mathrm{lift}(X\Rightarrow Y) = \frac{ \mathrm{supp}(X \cup Y)}{ \mathrm{supp}(X) \times \mathrm{supp}(Y) } </math>

or the ratio of the observed support to that expected if X and Y were [[Independence (probability theory)|independent]].

For example, the rule <math>\{\mathrm{milk, bread}\} \Rightarrow \{\mathrm{butter}\}</math> has a lift of <math>\frac{0.2}{0.4 \times 0.4} = 1.25 </math>.

If the rule had a lift of 1, it would imply that the probability of occurrence of the antecedent and that of the consequent are independent of each other. When two events are independent of each other, no rule can be drawn involving those two events.

If the lift is > 1, that lets us know the degree to which those two occurrences are dependent on one another, and makes those rules potentially useful for predicting the consequent in future data sets.

If the lift is < 1, that lets us know the items are substitute to each other. This means that presence of one item has negative effect on presence of other item and vice versa.

The value of lift is that it considers both the support of the rule and the overall data set.<ref name=":0" />

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