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Briana Petty 2022-05-21 Answered
Meaning of P ( X Y ) P ( X ) P ( Y )
Imagine that we have a set Ω and X and Y are events that can happen, I mean, P ( X ) , P ( Y ) > 0. Then, what does it mean the ratio P ( X Y ) P ( X ) P ( Y ) ?
I know that P ( X Y ) P ( X ) P ( Y ) = P ( X | Y ) P ( X ) = P ( Y | X ) P ( Y ) and if that ratio is equal to 1 then X,Y are independent events, but I can't figure out what exactly it means... please give simple examples.
I found this when reading about lift-data mining.
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Answers (1)

Samuel Vang
Answered 2022-05-22 Author has 12 answers
The ratio P ( X Y ) P ( X ) P ( Y ) = P ( X | Y ) P ( X ) is called lift, and it is a measure of how good the occurrence of event Y is at predicting the occurrence of event X. We interpret the lift as the ratio in which the probability of X increases after the occurrence of Y. Notice that P ( X c | Y ) P ( X c ) = 1 P ( X | Y ) 1 P ( X ) = 1 / P ( X ) lift 1 / P ( X ) 1 , which is 1 precisely when lift =1, and increases as lift increases. This is consistent with predicting the non occurrence of X after Y when lift <1.
Example: X is the event that this answer receives an up-vote. Y is the event that I provide an example. In this case we expect lift >1, as Y is presumably associated with an increased probability of X.
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