Computationally efficient segmentation for non-stationary time series with oscillatory patterns

2026-01-30

AI Summary

This work proposes an efficient and accurate method for change-point detection and parameter estimation in multivariate nonstationary time series containing oscillatory modes. By modeling the signal as a sum of piecewise sinusoidal functions plus noise and discretizing the parameter space—including frequencies—the problem is recast as a linear regression model based on Fourier bases, thereby enabling compatibility with existing change-point detection algorithms. The approach circumvents computationally intensive trans-dimensional Markov chain Monte Carlo sampling, achieving an order-of-magnitude speedup in simulations while maintaining localization accuracy comparable to state-of-the-art methods. Moreover, it provides high-probability bounds on change-point localization error. Empirical evaluations demonstrate its effectiveness on real-world climate data and EEG sleep signals.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Search and Optimization: Mixed Discrete/Continuous Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

We propose a novel approach for change-point detection and parameter learning in multivariate non-stationary time series exhibiting oscillatory behaviour. We approximate the process through a piecewise function defined by a sum of sinusoidal functions with unknown frequencies and amplitudes plus noise. The inference for this model is non-trivial. However, discretising the parameter space allows us to recast this complex estimation problem into a more tractable linear model, where the covariates are Fourier basis functions. Then, any change-point detection algorithms for segmentation can be used. The advantage of our proposal is that it bypasses the need for trans-dimensional Markov chain Monte Carlo algorithms used by state-of-the-art methods. Through simulations, we demonstrate that our method is significantly faster than existing approaches while maintaining comparable numerical accuracy. We also provide high probability bounds on the change-point localization error. We apply our methodology to climate and EEG sleep data.

Problem

• non-stationary time series
• oscillatory patterns
• change-point detection
• segmentation
• computational efficiency

Innovation

• change-point detection
• non-stationary time series
• oscillatory patterns
• Fourier basis
• computationally efficient segmentation