Distribution-free inference on the number of changepoints

• URL: http://arxiv.org/abs/2609.08234v1
• Date: Tue, 08 Sep 2026 04:26:54 GMT
• Title: Distribution-free inference on the number of changepoints
• Abstract summary: We show that a distribution-free upper confidence bound on $K$ must be trivial and uninformative.<n>We construct a finite-sample valid lower confidence bound on $K$, which we call the Conformal LOwer bound on Changepoint Count (CLOCC)
• Score: 36.191356601153146
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Suppose we are given an ordered sequence of independent data whose distribution changes $K$ times at unknown locations, for some unknown $K \geq 0$. In this paper, we study the problem of performing distribution-free inference on $K$. First, we show an impossibility result: any distribution-free upper confidence bound on $K$ must be trivial and uninformative. Then, using conformal $p$-values, and under only the assumption that the data segments induced by the changepoints are exchangeable (within themselves) and mutually independent, we construct a finite-sample valid lower confidence bound on $K$, which we call the Conformal LOwer bound on Changepoint Count (CLOCC). We show that CLOCC is the only feasible way to provide a lower bound on $K$ under the stated assumptions, a property we refer to as its universality. We provide practical guidelines for choosing score functions that yield efficient and tight lower bounds. We evaluate CLOCC in several synthetic and real-data experiments, where it provides informative lower bounds on $K$, demonstrating its practical applicability.

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