# Tutorial: How to establish quality and correctness of classification models? Part 5 – Lift curve

In this last part of the tutorial we will discuss the LIFT curve.

### Definition and types of lift curves

A lift chart pictures gains from applying a classification model in comparison to not applying it (i.e. using a random classifier) for a given section of data.

Two simple examples are shown below. 4 types of LIFT curves can be considered.

LIFT with percentage scale

• accumulated
• non-accumulated

LIFT with quotient scale

• accumulated
• non-accumuated

### How to construct a LIFT curve?

In order to construct a LIFT curve one needs to sort all the observation according to the decreasing scores generated by our model. In the example below we sort the values in the second column. We determine the number of quantiles, into which our observations will be divided. For instance, when dividing into quartiles, i.e. quantiles of orders ¼, ½, ¾ we get:

• 1st quartile divides the set of observations into two parts, 25% of values below this quartile and 75% of values above
• 2nd quartile divides the set of observations into two equal parts, in which the all the values in the first part are better than all the values in the second part
• 3rd quartile divides the set of observations into two parts, 75% of values below the values below this quartile and 25 % of values above

The number of quantiles is significant:

• If the quantiles are too small, the generated LIFT chart will be less comprehensible and reliable
• If the quantiles are too large, the LIFT chart will not be detailed enough

Next we display the concentration of positive observations (e.g. churn) in each quantile.

### Accumulated LIFT with percentage scale

General description Concrete example – sending new offer to customers ### Non-accumulated LIFT with percentage scale

General description Concrete example – sending new offer to customers Perfect classifiers ### Accumulated LIFT with quotient scale

General description Concrete example – sending new offer to customers ### Non-accumulated LIFT with quotient scale

General description Concrete example: sending new offer to customers ### Conclusions

• LIFT chart displays the gain from applying the given classifier in comparison to using a random classifier
• By dividing the values of the LIFT chart with percentage scale by the apriori probability we obtain a LIFT chart with quotient scale

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