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I frequently hear up- or down-sampling of data discussed as a way of dealing with classification of imbalanced data.

I understand that this could be useful if you're working with a binary (as opposed to probabilistic or score-based) classifier and treating it as a black box, so sampling schemes are your only way to tweak its position on the "ROC curve" (in quotes because if your classifier is inherently binary I guess it doesn't have a real ROC curve, but the same concept of trading off false positives and false negatives still applies).

But it seems like the same justification doesn't hold if you actually have access to some kind of score that you're later thresholding to make a decision. In this case, isn't up-sampling just an ad-hoc way of expressing a view about your desired trade-off between false positives and false negatives when you have much better tools available, like actual ROC analysis? It seems like it would be weird in this case to expect up-sampling or down-sampling to do anything but change your classifier's "prior" on each class (i.e. unconditional probability of being that class, the baseline prediction)--I wouldn't expect it to change the classifier's "odds ratio" (how much the classifier adjusts its baseline prediction based on the covariates).

So my question is: if you have a classifier that isn't a binary black box, are there any reasons to expect up- or down-sampling to have a much better effect than adjusting the threshold to your liking? Failing that, are there any empirical studies showing reasonably large effects for up- or down-sampling on reasonable performance metrics (e.g., not accuracy)?

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If you want to first to collect sample to do classification based on these results, then undersampling might be necessary even from the cost perpective.

But in this case your estimation methods typically do not return population level probabilities, they are conditional on the sampling scheme which was used.

Here is example:

https://stats.stackexchange.com/questions/127476/inference-possibilities-for-matched-case-control-study

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  • $\begingroup$ Sure. I'm more wondering about downsampling data that you already have, though, rather than undersampling during data collection. $\endgroup$ – Ben Kuhn Dec 12 '14 at 17:03

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