Is it possible to calibrate the probabilities of a binary classifier when the class priors are unknown?

In cases where the data is obtained with selection bias (i.e. more positives than negatives in data collection, but in actuality, there are more negatives than positives as an example), without full knowledge of the proportions, how do we calibrate the model?

This question is also applicable in the case of Positive Unlabeled learning, where if we had limited positives samples, but a variable amount of unlabeled data, how do we calibrate the probabilities of such a model?


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