Exact Multiple Change-Point Detection Via Smallest Valid Partitioning

TL;DR

This paper presents a novel segmentation method called smallest valid partitioning (SVP) for multiple change-point detection in time-series, emphasizing segment validity and computational efficiency.

Contribution

The paper introduces SVP, a new change-point detection approach that incorporates segment validity tests and a lexicographic optimization to improve segmentation accuracy.

Findings

SVP achieves competitive segmentation results compared to standard methods.

SVP enforces explicit segment validity, enhancing robustness.

Computational complexity varies from linear to cubic depending on parameters.

Abstract

We introduce smallest valid partitioning (SVP), a segmentation method for multiple change-point detection in time-series. SVP relies on a local notion of segment validity: a candidate segment is retained only if it passes a user-chosen validity test (e.g., a single change-point test). From the collection of valid segments, we propose a coherent aggregation procedure that constructs a global segmentation which is the exact solution of an optimization problem. Our main contribution is the use of a lexicographic order for the optimization problem that prioritizes parsimony. We analyze the computational complexity of the resulting procedure, which ranges from linear to cubic time depending on the chosen cost and validity functions, the data regime and the number of detected changes. Finally, we assess the quality of SVP through comparisons with standard optimal partitioning algorithms, showing that SVP yields competitive segmentations while explicitly enforcing segment validity. The flexibility of SVP makes it applicable to a broad class of problems; as an illustration, we demonstrate robust change-point detection by encoding robustness in the validity criterion.