Split-and-Conquer: Distributed Factor Modeling for High-Dimensional Matrix-Variate Time Series

2026-01-16

AI Summary

This study addresses the challenges of dimensionality reduction and modeling for high-dimensional, large-scale, heterogeneous matrix-valued time series by proposing a distributed two-dimensional tensor factor model. The approach partitions the data matrix into row and column blocks distributed across local nodes, where tensor PCA is applied locally to estimate loading matrices; a central server then aggregates these estimates and performs global PCA to recover the underlying latent structure. By preserving the native matrix format, the framework substantially enhances computational efficiency and information utilization, while also accommodating row-column clustering under unknown group structures and extending to nonstationary unit-root settings. Theoretical analysis establishes asymptotic properties under simultaneous growth of both dimensionality and sample size, and both simulations and empirical applications demonstrate superior performance in estimation accuracy and predictive power.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems
• 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
• Security and Privacy: Large-scale security measurements

Abstract

In this paper, we propose a distributed framework for reducing the dimensionality of high-dimensional, large-scale, heterogeneous matrix-variate time series data using a factor model. The data are first partitioned column-wise (or row-wise) and allocated to node servers, where each node estimates the row (or column) loading matrix via two-dimensional tensor PCA. These local estimates are then transmitted to a central server and aggregated, followed by a final PCA step to obtain the global row (or column) loading matrix estimator. Given the estimated loading matrices, the corresponding factor matrices are subsequently computed. Unlike existing distributed approaches, our framework preserves the latent matrix structure, thereby improving computational efficiency and enhancing information utilization. We also discuss row- and column-wise clustering procedures for settings in which the group memberships are unknown. Furthermore, we extend the analysis to unit-root nonstationary matrix-variate time series. Asymptotic properties of the proposed method are derived for the diverging dimension of the data in each computing unit and the sample size $T$. Simulation results assess the computational efficiency and estimation accuracy of the proposed framework, and real data applications further validate its predictive performance.

Problem

• matrix-variate time series
• dimensionality reduction
• factor modeling
• high-dimensional data
• distributed computing

Innovation

• distributed factor modeling
• matrix-variate time series
• tensor PCA
• split-and-conquer
• high-dimensional inference