Distribution-free inference on the number of changepoints
Abstract
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.
Related
- Impossibility of Distribution-Free Predictive Inference for Individual Treatment Effects
- Conformal ordering: Distribution-free predictive inference for orders and rank
- Distribution-free predictive inference with instrumental variables
- Distribution-Free Changepoint Inference for Rainfall Patterns
- Statistical inference and applications of Kumaraswamy Odd Perks power Lomax distribution
BibTeX
@misc{hore2026distributionfree,
title = {{Distribution-free inference on the number of changepoints}},
author = {Rohan Hore and Aaditya Ramdas},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08234},
eprint = {2609.08234},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08234},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Distribution-free inference on the number of changepoints
AU - Rohan Hore
AU - Aaditya Ramdas
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08234
UR - https://arxiv.org/abs/2609.08234
AB - 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.
ER -