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Old 10-31-2012, 12:03 PM
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yaser yaser is offline
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Location: Pasadena, California, USA
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Default Re: Covariate Shift in Data

Originally Posted by sagihaider View Post
Dear Professor,

I have one question,
According to your slide.No.4 and page 14, "The Learning Diagram-with error".

Question. If we talk about covariate shift, in this the input probability distribution changes in training input and test input, but the functional relationship remains same. i.e [p(train(x)) Not equal to p(test(x))] but p(y,x) remains unchanged. In different words (covariate shifts is when only the distribution of covariates x change and everything remains same)

Then how should we modify you diagram in term of probability distribution, to show the covariate shift.
This is an interesting question, and is the subject of some results in the literature as well as current research. In cases where we have different probability distributions for training and testing, there are methods to "match" the two distributions by giving weights to the training data points to tilt them towards the test distribution. If the distributions are known, this is fairly straightforward. If they are not known, there are still methods to do that with some interesting theoretical ramifications.

BTW, in the Netflix competition, this was a significant issue.
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