Testing for concept shift online

This note continues study of exchangeability martingales, i.e., processes that are martingales under any exchangeable distribution for the observations. Such processes can be used for detecting violations of the IID assumption, which is commonly made in machine learning. Violations of the IID assumption are sometimes referred to as dataset shift, and dataset shift is sometimes subdivided into concept shift, covariate shift, etc. Our primary interest is in concept shift, but we will also discuss exchangeability martingales that decompose perfectly into two components one of which detects concept shift and the other detects what we call label shift. Our methods will be based on techniques of conformal prediction.