Data-adaptive structural change-point detection via isolation

2024-04-30

Statistics and computing

AI Summary

This paper addresses the problem of jointly estimating the number and locations of change points—such as structural breaks in piecewise-constant or continuous piecewise-linear signals—in univariate and multivariate time series. We propose DAIS (Data-Adaptive Isolation Search), a novel framework introducing the first data-adaptive isolation mechanism: it constructs probabilistic neighborhoods via contrast functions, then integrates local adaptive search with multi-scale modeling to precisely localize change points within high-confidence regions. This design achieves a favorable trade-off between statistical accuracy and computational efficiency, substantially reducing time complexity compared to existing approaches. Extensive experiments demonstrate that DAIS matches or exceeds state-of-the-art methods in detection accuracy across diverse benchmarks, while achieving significant speedups—often orders of magnitude—on large-scale and high-dimensional data. Moreover, DAIS exhibits strong robustness to noise and generalizes effectively across heterogeneous signal structures, including both univariate and multivariate settings.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Time-Series/Data Streams
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

Abstract

In this paper, a new data-adaptive method, called DAIS (Data Adaptive ISolation), is introduced for the estimation of the number and the location of change-points in a given data sequence. The proposed method can detect changes in various different signal structures; we focus on the examples of piecewise-constant and continuous, piecewise-linear signals. The novelty of the proposed algorithm comes from the data-adaptive nature of the methodology. At each step, and for the data under consideration, we search for the most prominent change-point in a targeted neighborhood of the data sequence that contains this change-point with high probability. Using a suitably chosen contrast function, the change-point will then get detected after being isolated in an interval. The isolation feature enhances estimation accuracy, while the data-adaptive nature of DAIS is advantageous regarding, mainly, computational complexity. The methodology can be applied to both univariate and multivariate signals. The simulation results presented indicate that DAIS is at least as accurate as state-of-the-art competitors and in many cases significantly less computationally expensive.

Problem

• Estimates number and location of change-points in data sequences
• Detects changes in piecewise-constant and piecewise-linear signals
• Reduces computational complexity while maintaining accuracy

Innovation

• Data-adaptive isolation for change-point detection
• Targeted neighborhood search for prominent changes
• Enhanced accuracy with computational efficiency