Theoretical guarantees for change localization using conformal p-values

• URL: http://arxiv.org/abs/2510.08749v1
• Date: Thu, 09 Oct 2025 19:05:47 GMT
• Title: Theoretical guarantees for change localization using conformal p-values
• Authors: Swapnaneel Bhattacharyya, Aaditya Ramdas,
• Abstract summary: We provide theoretical guarantees for a method to achieve distribution-free changepoint localization with finite-sample validity.<n>We also present various finite sample and properties of the conformal $p$-value in the distribution change setup.<n>Our contributions offer a comprehensive and theoretically principled approach to distribution-free changepoint inference.
• Score: 36.191356601153146
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Changepoint localization aims to provide confidence sets for a changepoint (if one exists). Existing methods either relying on strong parametric assumptions or providing only asymptotic guarantees or focusing on a particular kind of change(e.g., change in the mean) rather than the entire distributional change. A method (possibly the first) to achieve distribution-free changepoint localization with finite-sample validity was recently introduced by \cite{dandapanthula2025conformal}. However, while they proved finite sample coverage, there was no analysis of set size. In this work, we provide rigorous theoretical guarantees for their algorithm. We also show the consistency of a point estimator for change, and derive its convergence rate without distributional assumptions. Along that line, we also construct a distribution-free consistent test to assess whether a particular time point is a changepoint or not. Thus, our work provides unified distribution-free guarantees for changepoint detection, localization, and testing. In addition, we present various finite sample and asymptotic properties of the conformal $p$-value in the distribution change setup, which provides a theoretical foundation for many applications of the conformal $p$-value. As an application of these properties, we construct distribution-free consistent tests for exchangeability against distribution-change alternatives and a new, computationally tractable method of optimizing the powers of conformal tests. We run detailed simulation studies to corroborate the performance of our methods and theoretical results. Together, our contributions offer a comprehensive and theoretically principled approach to distribution-free changepoint inference, broadening both the scope and credibility of conformal methods in modern changepoint analysis.

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