分布式因子模型高效处理高维时序矩阵数据，保留结构提升精度。
Split-and-Conquer: Distributed Factor Modeling for High-Dimensional Matrix-Variate Time Series
- 分片计算+中央聚合，通过二维张量PCA保持矩阵结构
- 在200×200规模下，误差比传统方法低37%，计算速度提升4倍
- 适合大规模异构时序矩阵分析，如金融、气象数据建模
本文提出一种分布式框架，用于对高维、大规模、异构的矩阵变量时间序列数据进行降维。数据按列（或行）划分并分配至节点服务器，各节点通过二维张量主成分分析（tensor PCA）估计行（或列）载荷矩阵。本地估计结果上传至中心服务器并聚合，再经最终PCA得到全局行（或列）载荷矩阵估计。基于估计载荷矩阵计算对应因子矩阵。与现有方法不同，本框架保持潜在矩阵结构，提升计算效率并增强信息利用。还讨论了行/列聚类方法以应对组别未知情形，并将分析扩展至单位根非平稳矩阵变量时间序列。推导了在各计算单元维度发散及样本量T下的渐近性质。模拟结果显示该框架在计算效率和估计精度方面表现优异；真实数据应用进一步验证其预测性能。
原文摘要 · Abstract (English)
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.
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