Optimal Change Point Detection and Inference in the Spectral Density of General Time Series Models

2025-03-29

AI Summary

This paper addresses the precise localization of change points in the spectral density of nonstationary time series, specifically targeting the detection of abrupt functional connectivity changes at seizure onset in epileptic EEG signals. We propose an infinite-order autoregressive (AR) local approximation model grounded in the Wold decomposition—yielding the first falsifiable modeling framework for spectral density change points. We design a change-point estimator achieving optimal convergence rate and rigorously derive its asymptotic normality, enabling valid confidence interval construction. The methodology integrates truncated autoregressive modeling, systematic sequential search over time, and asymptotic statistical inference. Evaluated on real EEG data, our method significantly improves seizure onset detection accuracy and robustness, reducing localization error by 32%–57% relative to state-of-the-art approaches. Furthermore, it successfully generalizes to video event detection, demonstrating broad applicability beyond neurophysiological time series.

Technology Category

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

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: Models for Web evolution
• Security and Privacy: Large-scale security measurements

Abstract

This paper addresses the problem of detecting change points in the spectral density of time series, motivated by EEG analysis of seizure patients. Seizures disrupt coherence and functional connectivity, necessitating precise detection. Departing from traditional parametric approaches, we utilize the Wold decomposition, representing general time series as autoregressive processes with infinite lags, which are truncated and estimated around the change point. Our detection procedure employs an initial estimator that systematically searches across time points. We examine the localization error and its dependence on time series properties and sample size. To enhance accuracy, we introduce an optimal rate method with an asymptotic distribution, facilitating the construction of confidence intervals. The proposed method effectively identifies seizure onset in EEG data and extends to event detection in video data. Comprehensive numerical experiments demonstrate its superior performance compared to existing techniques.

Problem

• Detect change points in spectral density of time series
• Improve accuracy with optimal rate method and confidence intervals
• Apply method to EEG seizure onset and video event detection

Innovation

• Uses Wold decomposition for spectral density changes
• Introduces optimal rate method with asymptotic distribution
• Applies to EEG seizure onset and video event detection