Selective review of offline change point detection methods (1801.00718v3)

Abstract: This article presents a selective survey of algorithms for the offline detection of multiple change points in multivariate time series. A general yet structuring methodological strategy is adopted to organize this vast body of work. More precisely, detection algorithms considered in this review are characterized by three elements: a cost function, a search method and a constraint on the number of changes. Each of those elements is described, reviewed and discussed separately. Implementations of the main algorithms described in this article are provided within a Python package called ruptures.

• The paper provides a systematic review of offline change point detection methods by categorizing cost functions, search algorithms, and constraint strategies.
• It compares parametric models, which rely on assumptions like Gaussian shifts, with flexible non-parametric techniques such as kernel-based methods.
• The study introduces the ruptures Python package, offering a practical framework for replicating and advancing change detection algorithms in various applications.

Selective Review of Offline Change Point Detection Methods

This paper by Truong, Oudre, and Vayatis provides a detailed survey of offline change point detection methods for multivariate time series. The work is structured to systematically analyze algorithms through three critical elements: cost function, search method, and constraints on change points.

Cost Functions and Signal Models

The authors categorize cost functions into parametric and non-parametric types:

1. Parametric Models: These include costs based on maximum likelihood estimation, often assuming data is iid with shifts in parameters such as mean or variance. Specific applications are explored under Gaussian distributions for detecting mean and scale shifts.
2. Non-parametric Models: Techniques like empirical cumulative distribution functions, rank statistics, and kernel-based models offer flexibility to detect changes without detailed distributional assumptions. Notably, the kernel-based approach aligns with methods to identify distribution changes using embeddings in reproducing kernel Hilbert spaces.

Each cost function aligns with a particular signal model, allowing practitioners to tailor detection methodologies based on data attributes and domain-specific requirements.

Search Methods: Optimal and Approximate Techniques

Search methods are divided into categories depending on their solution's optimality and computational feasibility:

• Optimal Methods: Dynamic programming techniques like the Opt algorithm provide exact solutions in scenarios where the number of changes is known. Despite their computational intensity ($\mathcal{O}(KT^2)$), these methods are robust for moderate-sized datasets.
• Approximate Methods: Algorithms such as binary segmentation and bottom-up approaches offer computational efficiency. While being faster, these methods yield approximate solutions that may lack the precision of their optimal counterparts.

The Pelt algorithm, particularly noteworthy, provides exact solutions under linear penalties, achieving efficiency both in time complex ($\mathcal{O}(T)$) and in managing datasets with increasing observations.

Constraints on the Number of Changes

When the number of change points is unknown, selecting an appropriate penalty function becomes crucial. The survey reviews linear penalties and more complex variants like the modified BIC, allowing adaptation to a variety of model assumptions and parameter settings.

The authors discuss strategies for parameter calibration within these penalty frameworks, including methods like cross-validation which aid in balancing model complexity with computational tractability.

Evaluation Metrics and Applicability

Evaluation of change point detection methods is essential for assessing their efficacy. Metrics discussed in the paper include AnnotationError, Hausdorff distance, and RandIndex. These measures provide quantitative assessments of segmentation accuracy and robustness, vital for method comparison across applications ranging from finance to bioinformatics.

Implementation: The Ruptures Package

A pivotal practical contribution of this paper is the introduction of the ruptures Python package, which encapsulates many surveyed algorithms. This tool facilitates experimentation and method development by providing a consistent and modular framework for change point detection.

Conclusion and Implications

The comprehensive review establishes a unified understanding of change point detection methodologies and emphasizes the need for adaptive approaches tailored to specific datasets and domains. The theoretical insights coupled with practical toolsets like ruptures enable researchers and practitioners to advance their applications in diverse fields ranging from climate science to industrial systems. Future prospects in AI could involve integrating these detection methods into broader machine learning workflows, especially in adaptive and real-time systems. Such integration could enhance the capability of AI models to dynamically respond to structural changes in data.