# 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?

• 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.

• 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
• @nik: Say it costs 1 in paper and postage to mail each customer. Naively, we could spend a $1000 mailing all 1000 customers and we expect 8% response, or 80 customers. Using the model, if we mail the top 30% based on their score (for a cost of 30% * 1000 *$1 = $300) then we expect to get 60% of the response (60% * 80 = 48 customers). Thus, the mail cost is only$300 now and we expect 48 customers. Next, we'd estimate how much profit is likely from each customer. We have Spend-$1000-get-80-customers vs Spend-$300-get-48-customers and which one we choose depends on profit-per-customer. – Josh Hemann Oct 17 '11 at 22:20
• @user1700890 The top chart is often labeled a cumulative gain chart, while the bottom chart is not the same as a cumulative lift chart (where the lift can never be lower than 1) but divides the data into ten separate bins. – RobertF Aug 7 '17 at 19:27

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 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

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 total number of transactions for C is 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 the probability of the then (consequent) given the if (antecedent) part. here's the link to the source article

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

Say we are using the example of a grocery store that is testing the validity of an association rule that has an antecedent and a consequent (for example: "If a customer buys bread, they will also buy butter").

If you look at all transactions, and examine one at random, the probability that that transaction contains the consequent is "Expected Confidence". If you look at all transactions that contain the antecedent, and select a random transaction from these, the probability that that transaction will contain the consequent is "Confidence". "Lift" is essentially the difference between these two. With lift, we can examine the relationship between two items that have high confidence (if confidence is low then lift is essentially irrelevant).

If they have high confidence and low lift, then we still know the items are frequently bought together but we do not know if the consequent is happening because of the antecedent or if it is just a coincidence (perhaps they are both purchased together often because they're both very popular products but don't have any kind of relationship to one another).

However, if the confidence and lift are both high, then we can reasonably assume that the consequent is happening due to the antecedent. The higher the lift gets, the lower the probability is that the relationship between the two items is just a coincidence. In mathematical terms:

Lift = Confidence / Expected Confidence

In our example, if the confidence of our rule was high and the lift was low, that would mean that a lot of customers are buying bread and butter, but we do not know if it's due to some special relationship between bread and butter or if bread and butter are just popular items individually and the fact that they often show up in grocery carts together is just a coincidence. If the confidence in our rule is high and the lift is high, this indicates a pretty strong correlation between the antecedent and the consequent, meaning that we can reasonably assume that customers are buying butter because of the fact that they are buying bread. The higher the lift is, the more confident we can be in this association.