Joint modeling and inference of multiple-subject high-dimensional sparse vector autoregressive models

2025-10-15

AI Summary

In multi-subject high-dimensional sparse vector autoregressive (VAR) models, existing weighted median approaches suffer from inefficient identification of shared effects, as convergence rates for both shared and subject-specific paths are bottlenecked by the least sparse subject and the smallest sample size. Method: We propose an identifiable shared–specific path decomposition framework, coupled with a communication-efficient data fusion mechanism that decouples convergence rates—aligning shared-path estimation with global sparsity structure and subject-specific paths with individual sparsity levels and sample sizes. Furthermore, we develop a debiased-estimation-based Wald-type inference framework for joint testing of shared and subject-specific Granger causality. Results: Extensive simulations and real-data analyses demonstrate that our method significantly outperforms state-of-the-art benchmarks in accuracy of path identification, statistical power of significance testing, and discrimination of effect homogeneity.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Matrix & Tensor Methods
• Computer Vision: Multi-modal Vision

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The multiple-subject vector autoregression (multi-VAR) model captures heterogeneous network Granger causality across subjects by decomposing individual sparse VAR transition matrices into commonly shared and subject-unique paths. The model has been applied to characterize hidden shared and unique paths among subjects and has demonstrated performance compared to methods commonly used in psychology and neuroscience. Despite this innovation, the model suffers from using a weighted median for identifying the common effects, leading to statistical inefficiency as the convergence rates of the common and unique paths are determined by the least sparse subject and the smallest sample size across all subjects. We propose a new identifiability condition for the multi-VAR model based on a communication-efficient data integration framework. We show that this approach achieves convergence rates tailored to each subject's sparsity level and sample size. Furthermore, we develop hypothesis tests to assess the nullity and homogeneity of individual paths, using Wald-type test statistics constructed from individual debiased estimators. A test for the significance of the common paths can also be derived through the framework. Simulation studies under various heterogeneity scenarios and a real data application demonstrate the performance of the proposed method compared to existing benchmark across standard evaluation metrics.

Problem

• Identifies heterogeneous network causality across multiple subjects
• Improves statistical efficiency in shared and unique path estimation
• Develops hypothesis tests for path nullity and homogeneity assessment

Innovation

• New identifiability condition for multi-VAR model
• Communication-efficient data integration framework approach
• Individual debiased estimators for hypothesis tests