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We are oversampling the data to use in logistic regression. Aim is to predict CTR(click probability) which is rare event scenario. I have predicted the probabilities of click but CTR results are inflated as we over sampled positive class.

model2<-SMOTE(V61 ~ ., z2, perc.over = 600,perc.under=100, learner = 'glm',family=binomial())

Is there any way to undo oversampling results so that I can get exact probabilities ? Based on research so far, one easiest way to divide the output probability by the multiplier we used in over sampling. I dont feel it would be the exact way as I have used synthetic minority over sampling technique(SMOTE) in R.

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  • $\begingroup$ Are you sure you need to oversample? Logistic regression does not suffer from an imbalance in classes. $\endgroup$ – Matthew Drury Jan 22 '17 at 0:28
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It doesn't work just to divide the probabilities. Basically you have to adjust the odds, not the probabilities.

There's a nice description and some sample calculations here: https://yiminwu.wordpress.com/2013/12/03/how-to-undo-oversampling-explained/

(added in edit) There's a different derivation that gives the same results here:

http://blog.data-miners.com/2009/09/adjusting-for-oversampling.html

That blog post is a bit simpler to understand.

I'm not a SMOTE user, and can't comment on the particular applicability to SMOTE.

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