Local Interaction Autoregressive Model for High Dimension Time Series Data

2025-11-12

AI Summary

High-dimensional matrix/tensor time series often exhibit local dependence, wherein each element interacts only with a limited set of variables within its spatiotemporal neighborhood. To address this, we propose the Local Interaction Autoregressive (LIAR) framework, which jointly identifies sparse local connectivity structures and estimates parameters efficiently. LIAR employs a separable model structure coupled with a BIC-type neighborhood selection criterion, ensuring consistent neighborhood recovery. We establish theoretical guarantees on neighborhood selection consistency and derive an error bound for covariance estimation. Parameter estimation leverages parallel least squares and kernel-based modeling of local dynamics, drastically reducing effective dimensionality. In simulations, LIAR accurately recovers true neighborhoods; applied to ionospheric Total Electron Content (TEC) data, it successfully captures spatiotemporal propagation patterns. Compared to state-of-the-art matrix time series models, LIAR achieves superior predictive accuracy and computational efficiency.

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: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

High-dimensional matrix and tensor time series often exhibit local dependency, where each entry interacts mainly with a small neighborhood. Accounting for local interactions in a prediction model can greatly reduce the dimensionality of the parameter space, leading to more efficient inference and more accurate predictions. We propose a Local Interaction Autoregressive (LIAR) framework and study Separable LIAR, a variant with shared row and column components, for high-dimensional matrix/tensor time series forecasting problems. We derive a scalable parameter estimation algorithm via parallel least squares with a BIC-type neighborhood selector. Theoretically, we show consistency of neighborhood selection and derive error bounds for kernel and auto-covariance estimation. Numerical simulations show that the BIC selector recovers the true neighborhood with high success rates, the LIAR achieves small estimation errors, and the forecasts outperform matrix time-series baselines. In real data applications, a Total Electron Content (TEC) case study shows the model can identify localized spatio-temporal propagation and improved prediction as compared with non-local time series prediction models.

Problem

• Modeling local dependencies in high-dimensional matrix/tensor time series data
• Reducing parameter dimensionality for efficient inference and accurate forecasting
• Developing scalable algorithms for neighborhood selection and parameter estimation

Innovation

• Local Interaction Autoregressive framework for high-dimensional data
• Scalable parallel least squares with BIC neighborhood selection
• Separable LIAR with shared row and column components