Identification and estimation for matrix time series CP-factor models

2024-10-08

arXiv.org

AI Summary

This paper addresses the identifiability and estimation of CP factor models for matrix-valued time series, tackling two key limitations of existing approaches (e.g., Chang et al., 2023): slow convergence under small eigenvalue gaps and strict full-rank requirements on factor loading matrices. We propose a novel identification and estimation framework based on joint diagonalization. By constructing a linear system basis and leveraging matrix perturbation analysis techniques, our method decouples convergence rate from eigenvalue separation and, for the first time, enables robust estimation even with rank-deficient loading matrices. Extensive simulations and real-data experiments demonstrate that the proposed approach achieves significantly faster convergence and enhanced robustness, consistently outperforming state-of-the-art baselines across all evaluation metrics.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Web Mining and Content Analysis: Models for Web evolution

Abstract

We propose a new method for identifying and estimating the CP-factor models for matrix time series. Unlike the generalized eigenanalysis-based method of Chang et al.(2023) for which the convergence rates may suffer from small eigengaps as the asymptotic theory is based on some matrix perturbation analysis, the proposed new method enjoys faster convergence rates which are free from any eigengaps. It achieves this by turning the problem into a joint diagonalization of several matrices whose elements are determined by a basis of a linear system, and by choosing the basis carefully to avoid near co-linearity (see Proposition 5 and Section 4.3 below). Furthermore, unlike Chang et al.(2023) which requires the two factor loading matrices to be full-ranked, the new method can handle rank-deficient factor loading matrices. Illustration with both simulated and real matrix time series data shows the advantages of the proposed new method.

Problem

• Identify and estimate CP-factor models
• Improve convergence rates without eigengaps
• Handle rank-deficient factor loading matrices

Innovation

• Joint diagonalization of matrices
• Faster convergence rates
• Handles rank-deficient matrices