Detecting and localizing changepoints without distributional assumptions
We revisit a classical problem of identifying the location of a changepoint in a given sequence of N independent observations, but from a modern distribution-free lens. Our algorithm, CONformal CHangepoint localization (CONCH) produces a confidence set for the index at which a change occurs without making any assumptions about the distributions before or after the change, or on the underlying space (e.g., text, images, etc.). Existing methods often rely on parametric assumptions, tail conditions, or asymptotic approximations, or only produce point estimates. By proving a conformal Neyman-Pearson lemma, we derive principled score functions that yield informative (small) sets, whose normalized length shrinks to zero under weak assumptions. We also establish a universality result showing that any distribution-free changepoint localization method must be an instance of CONCH. Experiments utilizing pre-trained classifiers suggest that CONCH delivers precise confidence sets even in challenging settings involving images or text.