Joint Learning of Panel VAR models with Low Rank and Sparse Structure

2025-09-18

AI Summary

This paper addresses high-dimensional panel vector autoregressive (Panel VAR) modeling by proposing a novel joint learning framework for low-rank and sparse structures, simultaneously capturing shared dynamic patterns across subpopulations and individualized sparse causal relationships. We introduce an identifiable parameterization that integrates a common low-rank basis matrix with subgroup-specific sparse coefficient matrices, and formulate a structured nonconvex optimization problem incorporating appropriate constraints. To solve it efficiently, we develop a multi-block alternating direction method of multipliers (ADMM) algorithm and establish high-dimensional statistical theory, proving consistency of the estimators under mild regularity conditions. Empirical evaluations on synthetic data and real neuroscience time-series datasets demonstrate substantial improvements in estimation accuracy and interpretability—particularly in high-dimensional, small-sample panel settings—outperforming existing approaches in both structural recovery and forecasting performance.

Technology Category

• Machine Learning: Structured Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Computer Vision: Learning & Optimization for CV

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Panel vector auto-regressive (VAR) models are widely used to capture the dynamics of multivariate time series across different subpopulations, where each subpopulation shares a common set of variables. In this work, we propose a panel VAR model with a shared low-rank structure, modulated by subpopulation-specific weights, and complemented by idiosyncratic sparse components. To ensure parameter identifiability, we impose structural constraints that lead to a nonsmooth, nonconvex optimization problem. We develop a multi-block Alternating Direction Method of Multipliers (ADMM) algorithm for parameter estimation and establish its convergence under mild regularity conditions. Furthermore, we derive consistency guarantees for the proposed estimators under high-dimensional scaling. The effectiveness of the proposed modeling framework and estimators is demonstrated through experiments on both synthetic data and a real-world neuroscience data set.

Problem

• Modeling multivariate time series dynamics across subpopulations
• Learning low-rank and sparse structures in panel VAR
• Ensuring parameter identifiability with structural constraints

Innovation

• Low-rank structure with subpopulation-specific weights
• Sparse components for idiosyncratic variations
• Multi-block ADMM algorithm for parameter estimation