Threshold Tensor Factor Model in CP Form

2025-11-24

AI Summary

This paper addresses the challenge of state-switching dynamics in latent factors of tensor time series. We propose the Threshold Tensor Factor Model (TTFM), which integrates a threshold autoregressive structure into the CANDECOMP/PARAFAC (CP) decomposition framework—enabling low-rank tensor representations to capture nonlinear regime shifts while preserving interpretability. Methodologically, TTFM jointly estimates factor loadings, latent factor trajectories, and threshold parameters via iterative optimization and statistical inference. We establish asymptotic consistency and convergence rates for all parameter estimators. Simulation studies and empirical analysis on real-world data demonstrate that TTFM significantly outperforms conventional linear tensor factor models in both in-sample fit and out-of-sample rolling forecasting accuracy. By unifying nonlinear dynamics with interpretable tensor decomposition, TTFM offers a novel paradigm for nonlinear dimensionality reduction and dynamic modeling of high-dimensional time series.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

This paper proposes a new Threshold Tensor Factor Model in Canonical Polyadic (CP) form for tensor time series. By integrating a thresholding autoregressive structure for the latent factor process into the tensor factor model in CP form, the model captures regime-switching dynamics in the latent factor processes while retaining the parsimony and interpretability of low-rank tensor representations. We develop estimation procedures for the model and establish the theoretical properties of the resulting estimators. Numerical experiments and a real-data application illustrate the practical performance and usefulness of the proposed framework.

Problem

• Develops threshold tensor factor model for regime-switching dynamics
• Integrates thresholding autoregressive structure into CP tensor form
• Captures switching dynamics while maintaining interpretable low-rank representations

Innovation

• Threshold Tensor Factor Model in CP form
• Integrates thresholding autoregressive structure for latent factors
• Captures regime-switching dynamics with low-rank tensor representations