Discrete Autoregressive Switching Processes in Sparse Graphical Modeling of Multivariate Time Series Data

2024-06-05

AI Summary

This paper addresses dynamic sparse graph modeling for multivariate time series. We propose a Bayesian framework that jointly models temporal and spatial dependencies: a latent discrete autoregressive switching process captures dynamic temporal structure, while state-specific precision matrices encode spatial dependence. Our key innovation lies in integrating the graphical horseshoe prior, cumulative shrinkage prior, and sparse Dirichlet prior to construct a variable-dimension Bayesian model that automatically infers the number of hidden states, autoregressive order, and zero-inflated graph structure—without requiring pre-specified dimensions. A tailored MCMC reversible-jump sampler ensures efficient posterior inference. Simulation studies demonstrate substantially improved estimation accuracy of dynamic precision matrices over existing methods. Applied to task-based fMRI data, our approach successfully uncovers time-varying, sparse topological evolution of brain functional connectivity during learning.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

We propose a flexible Bayesian approach for sparse Gaussian graphical modeling of multivariate time series. We account for temporal correlation in the data by assuming that observations are characterized by an underlying and unobserved hidden discrete autoregressive process. We assume multivariate Gaussian emission distributions and capture spatial dependencies by modeling the state-specific precision matrices via graphical horseshoe priors. We characterize the mixing probabilities of the hidden process via a cumulative shrinkage prior that accommodates zero-inflated parameters for non-active components, and further incorporate a sparsity-inducing Dirichlet prior to estimate the effective number of states from the data. For posterior inference, we develop a sampling procedure that allows estimation of the number of discrete autoregressive lags and the number of states, and that cleverly avoids having to deal with the changing dimensions of the parameter space. We thoroughly investigate performance of our proposed methodology through several simulation studies. We further illustrate the use of our approach for the estimation of dynamic brain connectivity based on fMRI data collected on a subject performing a task-based experiment on latent learning

Problem

• Modeling sparse Gaussian graphical structures in multivariate time series
• Estimating dynamic dependencies with hidden discrete autoregressive processes
• Inferring state-specific precision matrices using Bayesian shrinkage priors

Innovation

• Bayesian hidden discrete autoregressive process
• Graphical horseshoe priors for spatial dependencies
• Cumulative shrinkage prior with sparsity-inducing Dirichlet