# Lift measure in data mining

I searched many websites to know what exactly lift will do? The results that I found all were about using it in applications not itself.

I know about the support and confidence function. From Wikipedia, in data mining, lift is a measure of the performance of a model at predicting or classifying cases, measuring against a random choice model. But how? Confidence*support is the value of lift I searched another formulas too but I can't understand why the lift charts are important in accuracy of predicted values I mean I want to know what policy and reason is behind lift?

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Need context here. In marketing, this would be a chart which would indicate the percent sales increase expected from various marketing activities, but you probably have a different context in mind. – zbicyclist Jun 26 '12 at 18:24

I'll give an example of how "lift" is useful...

Imagine you are running a direct mail campaign where you mail customers an offer in the hopes they respond. Historical data shows that when you mail your customer base completely at random about 8% of them respond to the mailing (i.e. they come in and shop with the offer). So, if you mail 1,000 customers you can expect 80 responders.

Now, you decide to fit a logistic regression model to your historical data to find patterns that are predictive of whether a customer is likely to respond to a mailing. Using the logistic regression model each customer is assigned a probability of responding and you can assess the accuracy because you know whether they actually responded. Once each customer is assigned their probability, you rank them from highest to lowest scoring customer. Then you could generate some "lift" graphics like these:

Ignore the top chart for now. The bottom chart is saying that after we sort the customers based on their probability of responding (high to low), and then break them up into ten equal bins, the response rate in bin #1 (the top 10% of customers) is 29% vs 8% of random customers, for a lift of 29/8 = 3.63. By the time we get to scored customers in the 4th bin, we have captured so many the previous three that the response rate is lower than what we would expect mailing people at random.

Looking at the top chart now, what this says is that if we use the probability scores on customers we can get 60% of the total responders we'd get mailing randomly by only mailing the top 30% of scored customers. That is, using the model we can get 60% of the expected profit for 30% of the mail cost by only mailing the top 30% of scored customers, and this is what lift really refers to.

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+1 Nicely illustrated and explained, Josh. – whuber Oct 17 '11 at 16:21
Nice explanation thank you so much.would you please tell me in the Lift chart why we need random sample? I understood 8% is from random but why it is needed to trace random? I saw another chart that traces the average of values and i don't know the reason of existence of average either – Nickool Oct 17 '11 at 19:14
the thing that i got is that lift=3.63 is saying that until column 4 we have better response rates than 8% well,then you just assume the column 1 and by considering 29%(30% in estimate) you just considered the column 1. then what lift did with 3.63? – Nickool Oct 17 '11 at 19:33
Oh my God! I understood my mistake the 30% doesn't relate to the 29% the 30% means 3/10 3 first columns of Data! Now I completely understood it:D I am so happy!!!!! thank you>:D< – Nickool Oct 17 '11 at 19:49
sorry all! that I commented too much! Josh would you please tell me about this sentence we can get 60% of the expected profit for 30% of the mail cost by only mailing the top 30% of scored customers I can't understand here (30 % of the mail cost) this 30% is which one? why you mentioned two 30%? 30% of top is from the lift and this 30% is from where? – Nickool Oct 17 '11 at 20:21

lift charts represent the ratio between the response of a model vs the absence of that model. Typically it's represented by the percentage of cases in the X and the number of times the response is better in the Y axe. For example a model with a lift 2 at the point 10% means:

-Without any model taking a 10% of the population (with no order because no model) the proportion of y=1 would be 10% of the total population with y=1. -With the model we get 2 times this proportion, i.e, we expect to get 20% of the total population with y=1.In th char label X represents data orderd by the prediction. THe first 10% is the top 10% predictions

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Lift is just a measure to measure the importance of the rule

its a measure to check whether this rule is in the list by random chance or we are expecting

Lift = Confidence / Expected Confidence

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Lift is nothing but the ratio of Confidence to Expected Confidence.In the area of association rules - "A lift ratio larger than 1.0 implies that the relationship between the antecedent and the consequent is more significant than would be expected if the two sets were independent. The larger the lift ratio, the more significant the association." For Example-

if a supermarket database has 100,000 point-of-sale transactions, out of which 2,000 include both items A and B, and 800 of these include item C, the association rule "If A and B are purchased, then C is purchased on the same trip," has a support of 800 transactions (alternatively 0.8% = 800/100,000), and a confidence of 40% (=800/2,000). One way to think of support is that it is the probability that a randomly selected transaction from the database will contain all items in the antecedent and the consequent, whereas the confidence is the conditional probability that a randomly selected transaction will include all the items in the consequent, given that the transaction includes all the items in the antecedent.

Using the above example, expected Confidence in this case means, "confidence, if buying A and B does not enhance the probability of buying C." It is the number of transactions that include the consequent divided by the total number of transactions. Suppose the number of total number of transactions for C are 5,000. Thus Expected Confidence is 5,000/1,00,000=5%. For the supermarket example the Lift = Confidence/Expected Confidence = 40%/5% = 8. Hence, Lift is a value that gives us information about the increase in probability of the then (consequent) given the if (antecedent) part.

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