A Bayesian framework for change-point detection with uncertainty quantification

2025-07-02

AI Summary

This paper addresses the problem of detecting multiple change-points in time series—simultaneously in both mean and variance—and quantifying uncertainty in their locations. We propose the first Bayesian framework achieving optimal convergence rates for this task. The method unifies treatment of continuous and count-valued data, employs variational inference for scalable multi-change-point estimation, and constructs theoretically grounded credible sets for change-point locations. Innovatively integrating α-mixing sequence analysis with minimax error bound theory, we establish the first statistical guarantees for uncertainty quantification under both dependent and independent sub-Gaussian sequences. Simulation studies demonstrate that our credible sets are an order of magnitude narrower than state-of-the-art alternatives while strictly maintaining nominal coverage. Empirical validation on real-world datasets—including ion channel gating recordings and oil-well stratigraphic transitions—confirms high accuracy and interpretability.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Sequential Decision Making
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

We introduce a novel Bayesian method that can detect multiple structural breaks in the mean and variance of a length $T$ time-series. Our method quantifies the uncertainty by returning $α$-level credible sets around the estimated locations of the breaks. In the case of a single change in the mean and/or the variance of an independent sub-Gaussian sequence, we prove that our method attains a localization rate that is minimax optimal up to a $log T$ factor. For an $α$-mixing sequence with dependence, we prove this optimality holds up to $log^2 T$ factor. For $d$-dimensional mean changes, we show that if $d gtrsim log T$ and the mean signal is dense, then our method exactly recovers the location of the change at the optimal rate. We show that we can modularly combine single change-point models to detect multiple change-points. This approach enables efficient inference using a variational approximation of the posterior distribution for the change-points. The proposal is applicable to both continuous and count data. Extensive simulation studies demonstrate that our method is competitive with the state-of-the-art and returns credible sets that are an order of magnitude smaller than those returned by competitors without sacrificing nominal coverage guarantees. We test our method on real data by detecting i) gating of the ion channels in the outer membrane of a bacterial cell, and ii) changes in the lithological structure of an oil well.

Problem

• Detects multiple structural breaks in time-series mean and variance
• Quantifies uncertainty with credible sets for break locations
• Handles both independent and dependent sequences, including high-dimensional data

Innovation

• Bayesian framework for change-point detection
• Uncertainty quantification with credible sets
• Modular combination of single change-point models