ART: Distribution-Free and Model-Agnostic Changepoint Detection with Finite-Sample Guarantees

TL;DR

ART provides a distribution-free, model-agnostic framework for changepoint detection with finite-sample guarantees by transforming observations into symmetric scores, ranking them, and aggregating ranks via Rank CUSUM or nonparametric likelihood methods. The approach extends to multi-scale settings, enabling robust multiple changepoint testing, localization with inference, and post-detection validation while maintaining exact size control through permutation-based and randomized p-values. The paper establishes theoretical results on distribution-freeness and pivotalness, proves consistency of localization, and demonstrates strong empirical performance on synthetic data and real-world tasks (well-log and MNIST), including high-dimensional and non-Euclidean scenarios. The methodology offers a flexible, scalable tool for modern changepoint analysis that integrates well with machine learning procedures and uncertainty quantification, without relying on strong distributional or model assumptions.

Abstract

We introduce ART, a distribution-free and model-agnostic framework for changepoint detection that provides finite-sample guarantees. ART transforms independent observations into real-valued scores via a symmetric function, ensuring exchangeability in the absence of changepoints. These scores are then ranked and aggregated to detect distributional changes. The resulting test offers exact Type-I error control, agnostic to specific distributional or model assumptions. Moreover, ART seamlessly extends to multi-scale settings, enabling robust multiple changepoint estimation and post-detection inference with finite-sample error rate control. By locally ranking the scores and performing aggregations across multiple prespecified intervals, ART identifies changepoint intervals and refines subsequent inference while maintaining its distribution-free and model-agnostic nature. This adaptability makes ART as a reliable and versatile tool for modern changepoint analysis, particularly in high-dimensional data contexts and applications leveraging machine learning methods.

Figures (8)

• Figure 1: A flowchart illustrating the procedure, key properties, and application scenarios of ART. Here, $\mathbb{P}^*\in\mathcal{H}_1$ characterizes the actual data distribution with changepoints $\{\tau^*_k\}_{k\in[K^*]}$, while $\mathbb{P}^*\in\mathcal{H}_0$ represents a hypothetical context without any changepoints; see Section \ref{['subsec:model']}.
• Figure 2: Empirical size and power of ART, DMS, and LZZL in mean change models with multiple changepoints under different error distributions. The red dashed line represents the nominal Type-I error.
• Figure 3: Comparisons of ART and TUNE (TUNE.Wald for (i) and TUNE.boots for (ii)) for post-detection inference under various error settings. The red dashed line represents the nominal FWER level.
• Figure 4: The gray dots show the well-log measurements, while the vertical lines mark the detected changepoints at $\alpha=0.1$. The horizontal lines display the median within each segment.
• Figure 5: Illustration of the four changepoint detection scenarios using the MNIST dataset.

Theorems & Definitions (25)

• Example 1: Changes in means
• Example 2: Changes in regression coefficients
• Definition 1: Symmetric transformation
• Theorem 1
• Example \ref{ex:reg}: Revisited; High-dimensional setting
• Theorem 2
• Corollary 1
• Theorem 3
• Theorem 4
• Proposition 1