In data mining and association rule learning,
lift is a measure of the performance of a
targeting model at predicting or classifying
cases as having an enhanced response, 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 has
identified a segment with a response rate
of 20%.
Then that segment would have a lift of 4.0.
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
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 as the target response probability.
The lift curve can also be considered a variation
on the receiver operating characteristic curve,
and is also known in econometrics as the Lorenz
or power curve.
The difference between the lifts observed
on two different subgroups is called the uplift.
The subtraction of two lift curves forms the
uplift curve, which is a metric used in uplift
modelling.
Example
Assume the data set being mined is:
where the antecedent is the input variable
that we can control, and the consequent is
the variable we are trying to predict.
Real mining problems would typically have
more complex antecedents, but usually focus
on single-value consequents.
Most mining algorithms would determine the
following rules:
Rule 1: A implies 0
Rule 2: B implies 1
because these are simply the most common patterns
found in the data.
A simple review of the above table should
make these rules obvious.
The support for Rule 1 is 3/7 because that
is the number of items in the dataset in which
the antecedent is A and the consequent 0.
The support for Rule 2 is 2/7 because two
of the seven records meet the antecedent of
B and the consequent of 1.
The supports can be written as:
The confidence for Rule 1 is 3/4 because three
of the four records that meet the antecedent
of A meet the consequent of 0.
The confidence for Rule 2 is 2/3 because two
of the three records that meet the antecedent
of B meet the consequent of 1.
The confidences can be written as:
Lift can be found by dividing the confidence
by the unconditional probability of the consequent,
or by dividing the support by the probability
of the antecedent times the probability of
the consequent, so:
The lift for Rule 1 is7) ≈ 1.31
The lift for Rule 2 is7) = 2/3 * 7/3 = 14/9
≈ 1.56
If some 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, like it is here for Rules
1 and 2, 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.
Observe that even though Rule 1 has higher
confidence, it has lower lift.
Intuitively, it would seem that Rule 1 is
more valuable because of its higher confidence—it
seems more accurate.
But accuracy of the rule independent of the
data set can be misleading.
The value of lift is that it considers both
the confidence of the rule and the overall
data set.
References
^ Tufféry, Stéphane; Data Mining and Statistics
for Decision Making, Chichester, GB: John
Wiley & Sons, translated from the French Data
Mining et statistique décisionnelle
^ Kuusisto, Finn; Santos Costa, Vitor; Nassif,
Houssam; Burnside, Elizabeth; Page, David;
Shavlik, Jude.
"Support Vector Machines for Differential
Prediction".
European Conference on Machine Learning. 
^ Nassif, Houssam; Kuusisto, Finn; Burnside,
Elizabeth; Shavlik, Jude.
"Uplift Modeling with ROC: An SRL Case Study".
International Conference on Inductive Logic
Programming. 
Coppock, David S..
"Data Modeling and Management: Why Lift?".
Retrieved 2007-02-19. 
See also
Uplift modelling
