# Distribution-free inference on the number of changepoints

arXiv: https://arxiv.org/abs/2609.08234 · HTML: https://mlsanity.com/paper/2609.08234/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 39 references that are in the map.
- First posted on arXiv 8 Sep 2026.

## Builds on (most cited first, 13 of 13)

- [Theoretical Foundations of Conformal Prediction](https://mlsanity.com/paper/2411.11824/) (2024)
- [E-detectors: a nonparametric framework for sequential change detection](https://mlsanity.com/paper/2203.03532/) (2022)
- [Inductive Conformal Martingales for Change-Point Detection](https://mlsanity.com/paper/1706.03415/) (2017)
- [On Optimal Multiple Changepoint Algorithms for Large Data](https://mlsanity.com/paper/1409.1842/) (2014)
- [Multiple Change-point Detection: a Selective Overview](https://mlsanity.com/paper/1512.04093/) (2015)
- [Random Forests for Change Point Detection](https://mlsanity.com/paper/2205.04997/) (2022)
- [Offline changepoint localization using a matrix of conformal p-values](https://mlsanity.com/paper/2505.00292/) (2025)
- [Asymptotic Distribution-Free Change-Point Detection for Multivariate and non-Euclidean Data](https://mlsanity.com/paper/1707.00167/) (2017)
- [Detecting multiple generalized change-points by isolating single ones](https://mlsanity.com/paper/1901.10852/) (2019)
- [Bootstrap confidence intervals for multiple change points based on moving sum procedures](https://mlsanity.com/paper/2106.12844/) (2021)
- [Gaussian Derivative Change-point Detection for Early Warnings of Industrial System Failures](https://mlsanity.com/paper/2410.22594/) (2024)
- [Distribution-free root cause analysis](https://mlsanity.com/paper/2605.21627/) (2026)
- [Conformal Changepoint Localization and Root Cause Analysis with Corrupted Observations](https://mlsanity.com/paper/2607.26481/) (2026)

## Abstract (arXiv)

Suppose we are given an ordered sequence of independent data whose distribution changes K times at unknown locations, for some unknown K ≥ 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.