Detection and Mode-Identification of Multiple Change Points in Tensor Factor Models

2026-04-13

AI Summary

This study addresses the challenge of detecting and attributing structural change points in high-dimensional tensor time series, where changes may affect only subsets of modes and involve complex inter-mode interactions. The authors propose a Tucker decomposition–based factor model that formally characterizes the identifiability of mode-specific change points and introduces a unified framework for simultaneous multi-change-point detection and mode attribution. By integrating low-rank tensor decomposition, an efficient change-point detection algorithm, and a tailored mode identification strategy, the method establishes consistency under weak moment conditions and substantially improves estimation accuracy of mode loading spaces in the post-segmentation stage. Empirical evaluations on both synthetic data and real-world datasets—including New York City taxi traffic and Fama–French portfolio returns—demonstrate superior performance in change-point detection and mode attribution.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Computer Vision: Multi-modal Vision
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

We study the problems arising from modeling high-dimensional tensor-valued time series under a Tucker decomposition-based factor model with multiple structural change points. First, we propose an algorithm for detecting the multiple change points, which utilizes the low-rank structure of the data for statistical and computational efficiency. Also, the multi-dimensional array setting poses unique challenges, as some changes are associated with a subset of the modes, and the changes in different modes may interact with one another. Recognizing these, we investigate the problem of identifying each change with the tensor modes post-segmentation. To this end, we formalize the mode-identifiability of each change and propose an algorithm for detecting the modes at which the data are undergoing a mode-identifiable shift. We establish the consistency of both change point detection and mode-identification methods under a weak moment condition, and demonstrate their good performance on simulated datasets where, in particular, it is shown that the mode-identification step can improve the post-segmentation estimation of the mode-wise loading space. Additionally we analyze the datasets on New York City taxi usage and Fama--French portfolio returns using the proposed suite of methods.

Problem

• change point detection
• tensor factor model
• mode identification
• structural change
• high-dimensional time series

Innovation

• tensor factor model
• multiple change points
• mode identifiability
• low-rank structure
• Tucker decomposition