# Association Rule Lift

An Association Rule Lift is an association rule performance measure that is the ratio between confidence measure $conf(X,\Rightarrow Y)$ and support measure $supp(X)$.

## References

### 2018a

• (Wikipedia, 2018) ⇒ https://en.wikipedia.org/wiki/Association_rule_learning#Lift Retrieved:2018-10-7.
• The lift of a rule is defined as: $\mathrm{lift}(X\Rightarrow Y) = \frac{ \mathrm{supp}(X \cup Y)}{ \mathrm{supp}(X) \times \mathrm{supp}(Y) }$ or the ratio of the observed support to that expected if X and Y were independent. For example, the rule $\{\mathrm{milk, bread}\} \Rightarrow \{\mathrm{butter}\}$ has a lift of $\frac{0.2}{0.4 \times 0.4} = 1.25$ .

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 confidence of the rule and the overall data set.

### 2018b

• (Wikipedia, 2018) ⇒ https://en.wikipedia.org/wiki/Lift_(data_mining) Retrieved:2018-10-7.
• In data mining and association rule learning, lift is a measure of the performance of a targeting model (association rule) at predicting or classifying cases as having an enhanced response (with respect to the population as a whole), measured against a random choice targeting model. A targeting model is doing a good job if the response within the target is much better than the average for the population as a whole. Lift is simply the ratio of these values: target response divided by average response.

For example, suppose a population has an average response rate of 5%, but a certain model (or rule) has identified a segment with a response rate of 20%. Then that segment would have a lift of 4.0 (20%/5%).

Typically, the modeller seeks to divide the population into quantiles, and rank the quantiles by lift. Organizations can then consider each quantile, and by weighing the predicted response rate (and associated financial benefit) against the cost, they can decide whether to market to that quantile or not.

Lift is analogous to information retrieval's average precision metric, if one treats the precision (fraction of the positives that are true positives) as the target response probability.

The lift curve can also be considered a variation on the receiver operating characteristic (ROC) curve, and is also known in econometrics as the Lorenz or power curve [1].