Exact Multiple Change-Point Detection Via Smallest Valid Partitioning

TL;DR

The paper proposes Smallest Valid Partitioning (SVP), a change-point detection framework that enforces segment-level validity via a local test and aggregates valid segments into a globally optimal segmentation using a lexicographic objective that first minimizes the number of segments and then the total cost. The approach is implemented via adaptive dynamic programming, yielding an exact solution with complexity that ranges from linear to cubic depending on the chosen cost and validity functions, and it includes pruning techniques to improve efficiency. SVP is demonstrated with parametric GLR-based (FOCuS) validity and non-parametric Wilcoxon and Mood validity tests, showing competitive performance to standard optimal partitioning methods while explicitly enforcing segment validity and offering robustness to outliers. The method is validated through simulations across mean-shift and heavy-tailed settings and applied to well-log data, highlighting its flexibility, robustness, and practical applicability for diverse change-point problems.

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.

Figures (9)

• Figure 1: An illustration of 4 examples of change patterns across the simulation scenarios, with a jump size of 0.6. Across the presented simulations, we range the jump size and vary the noise across replicates.
• Figure 2: F1 scores across the four simulation scenarios for PELT and SVP (with both likelihood and BIC penalties) as a function of jump size. Each point represents the average over 100 replications.
• Figure 3: F1 scores for robust change-point detection methods with heavy-tailed noise, across four scenarios as a function of jump size. Each point represents the average over 100 replications.
• Figure 4: Computational performance comparison between SVP and PELT.
• Figure 5: Well-log data segmentation. Results with 4 different methods

Theorems & Definitions (11)

• Proposition 1
• Definition 1
• Definition 2
• Lemma 1
• proof
• Proposition 2
• proof
• Proposition 3
• proof
• Proposition 4