[Paper Review] Change-point detection for multivariate and non-Euclidean data with local dependency

Hao Chen|arXiv (Cornell University)|Mar 5, 2019

Bayesian Methods and Mixture Models20 references4 citations

TL;DR

This paper proposes a circular block permutation with random starting point to improve change-point detection in multivariate and non-Euclidean data with local dependence. By integrating this permutation scheme into a nonparametric graph-based scan statistic framework, the method controls type I error under local dependence while maintaining high power, and provides an analytic p-value approximation for efficient computation on long sequences.

ABSTRACT

In a sequence of multivariate observations or non-Euclidean data objects, such as networks, local dependence is common and could lead to false change-point discoveries. We propose a new way of permutation -- circular block permutation with a random starting point -- to address this problem. This permutation scheme is studied on a non-parametric change-point detection framework based on a similarity graph constructed on the observations, leading to a general framework for change-point detection for data with local dependency. Simulation studies show that this new framework retains the same level of power when there is no local dependency, while it controls type I error correctly for sequences with and without local dependency. We also derive an analytic p-value approximation under this new framework. The approximation works well for sequences with length in hundreds and above, making this approach fast-applicable for long data sequences.

Motivation & Objective

• To address the issue of inflated type I error in change-point detection when observations exhibit local dependence.
• To develop a general, nonparametric framework for detecting change-points in high-dimensional or non-Euclidean data, such as networks or multivariate time series.
• To maintain statistical power under independence while correcting for false discoveries due to local dependence.
• To derive an analytic p-value approximation that enables fast computation on long data sequences.
• To provide a practical criterion for selecting the optimal block size in the circular block permutation scheme.

Proposed method

• Introduces circular block permutation with random starting point to preserve local dependence structure during resampling.
• Adapts the edge-count test within a scan statistic framework using a similarity graph constructed on pooled observations.
• Uses the maximum scan statistic across all possible change-point locations as the test statistic under the new permutation scheme.
• Derives an analytic approximation for the p-value of the test statistic, valid for sequences of length in the hundreds or more.
• Employs a block size selection rule based on convergence of the maximum scan statistic across increasing block sizes.
• Extends the framework to multiple change-points via recursive application of the single change-point method using binary or circular binary segmentation.

Experimental results

Research questions

• RQ1 How does local dependence affect the performance of existing nonparametric change-point detection methods based on permutation?
• RQ2 Can a modified permutation scheme preserve local dependence structure while maintaining correct type I error control?
• RQ3 What is the impact of block size on the accuracy and stability of the test statistic under local dependence?
• RQ4 Can an analytic p-value approximation be derived that is both accurate and computationally efficient for long sequences?
• RQ5 How can the proposed framework be extended to detect multiple change-points in complex data types?

Key findings

• The proposed circular block permutation with random starting point correctly controls type I error under both independent and locally dependent data, unlike standard permutation methods.
• The method maintains the same level of statistical power as the original method when observations are independent.
• The analytic p-value approximation is accurate for sequences of length 100 or more, enabling fast computation without extensive resampling.
• The maximum scan statistic stabilizes as block size increases, and a block size threshold can be identified using a ratio criterion (e.g., ratio > 0.99) to ensure sufficient dependence structure is captured.
• The framework successfully detects change-points in multivariate autoregressive and network data, even with strong serial correlation (e.g., ρ = 0.2).
• The extension to multiple change-points via recursive segmentation is feasible and effective, as demonstrated in simulation studies.