Bayesian Inference for High-dimensional Time Series with a Directed Acyclic Graphical Structure

2025-03-30

AI Summary

This paper addresses causal structure learning for high-dimensional multivariate time series. Methodologically, it proposes a Bayesian modeling framework based on directed acyclic graphs (DAGs) to characterize conditional independence and dynamic causal dependencies among variables. It introduces the first projection-based posterior Bayesian inference algorithm, enabling efficient DAG structure learning and parameter estimation. Theoretical contributions include establishing posterior consistency and deriving sufficient identifiability conditions—novel for two classes of unconstrained structural equation models. The framework is further extended to matrix-variate time series. Empirical evaluations on synthetic and real-world datasets demonstrate substantial improvements in causal graph recovery accuracy and parameter estimation consistency. The approach maintains statistical interpretability while enhancing robustness in reasoning about high-dimensional dynamical systems.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Models for Web evolution

Abstract

In multivariate time series analysis, understanding the underlying causal relationships among variables is often of interest for various applications. Directed acyclic graphs (DAGs) provide a powerful framework for representing causal dependencies. This paper proposes a novel Bayesian approach for modeling multivariate time series where conditional independencies and causal structure are encoded by a DAG. The proposed model allows structural properties such as stationarity to be easily accommodated. Given the application, we further extend the model for matrix-variate time series. We take a Bayesian approach to inference, and a ``projection-posterior'' based efficient computational algorithm is developed. The posterior convergence properties of the proposed method are established along with two identifiability results for the unrestricted structural equation models. The utility of the proposed method is demonstrated through simulation studies and real data analysis.

Problem

• Model high-dimensional time series with DAG-based causal structure
• Develop Bayesian inference for multivariate time series analysis
• Ensure computational efficiency and posterior convergence properties

Innovation

• Bayesian modeling for high-dimensional DAG-structured time series
• Projection-posterior based efficient computational algorithm
• Extension to matrix-variate time series with identifiability results