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

TL;DR

This paper introduces the RRNAR model, a low-rank autoregressive approach for high-dimensional multivariate network time series that captures complex interactions efficiently, with theoretical guarantees and practical improvements.

Contribution

The paper proposes a novel RRNAR model with a bilinear transition structure and a ScaledGD algorithm, providing theoretical error bounds and demonstrating improved performance on real network data.

Findings

Establishes non-asymptotic error bounds for the model.

Shows a network-induced blessing of dimensionality in sparse networks.

Demonstrates superior performance over benchmarks in traffic and server 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.