Distribution-free inference on the number of changepoints

2026-09-08

AI Summary

本文研究了在未知分布变化点位置的情况下，使用保形p值方法来推断变化点数量K的下限问题，提出了CLOCC方法。

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.

Problem

• distribution-free inference
• changepoints
• confidence bound

Innovation

• conformal p-values
• distribution-free inference
• changepoints
• CLOCC
• universality