Reduced-Rank Autoregressive Model for High-Dimensional Multivariate Network Time Series

2026-01-04

AI Summary

This work addresses the limitation of existing network autoregressive models, which treat nodes as scalar processes and thus fail to capture cross-variable interactions in high-dimensional multivariate network time series. To overcome this, we propose the Low-Rank Network Autoregressive (RRNAR) model, which integrates a known network topology with a learnable low-rank latent subspace through a separable bilinear transition structure. This design effectively captures cross-dimensional propagation mechanisms while avoiding the curse of dimensionality. Theoretical analysis reveals a “blessing of dimensionality”: under sparse network structures, estimation accuracy improves as the network size grows, and we establish non-asymptotic error bounds based on a novel distance metric. Coupled with a tailored Scaled Gradient Descent (ScaledGD) algorithm, RRNAR significantly outperforms baseline methods on real-world traffic and server monitoring datasets, successfully uncovering latent cross-channel propagation pathways.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Large Multimodal Models (LMMs)
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

Multivariate network time series are ubiquitous in modern systems, yet existing network autoregressive models typically treat nodes as scalar processes, ignoring cross-variable spillovers. To capture these complex interactions without the curse of dimensionality, we propose the Reduced-Rank Network Autoregressive (RRNAR) model. Our framework introduces a separable bilinear transition structure that couples the known network topology with a learnable low-rank variable subspace. We estimate the model using a novel Scaled Gradient Descent (ScaledGD) algorithm, explicitly designed to bridge the gap between rigid network scalars and flexible factor components. Theoretically, we establish non-asymptotic error bounds under a novel distance metric. A key finding is a network-induced blessing of dimensionality: for sparse networks, the estimation accuracy for network parameters improves as the network size grows. Applications to traffic and server monitoring networks demonstrate that RRNAR significantly outperforms univariate and unstructured benchmarks by identifying latent cross-channel propagation mechanisms.

Problem

• multivariate network time series
• cross-variable spillovers
• high-dimensional
• network autoregressive model
• dimensionality curse

Innovation

• Reduced-Rank Network Autoregressive
• Scaled Gradient Descent
• bilinear transition structure
• network-induced blessing of dimensionality
• multivariate network time series