Efficient Variational Bayes Learning of Graphical Models with Smooth Structural Changes

TL;DR

This paper introduces BASS, a low-complexity, tuning-free Bayesian method for estimating smooth, time-varying graphical models that outperforms existing approaches in accuracy and efficiency, especially in high-dimensional settings.

Contribution

The paper proposes BASS, a novel variational Bayesian approach with spike-and-slab priors for efficiently learning smooth, time-varying graphs without extensive parameter tuning.

Findings

BASS achieves lower computational complexity ($O(NP^2)$) compared to existing methods.

BASS more accurately recovers true graph structures in synthetic data.

BASS demonstrates superior performance on real datasets, especially in high-dimensional scenarios.

Abstract

Estimating time-varying graphical models are of paramount importance in various social, financial, biological, and engineering systems, since the evolution of such networks can be utilized for example to spot trends, detect anomalies, predict vulnerability, and evaluate the impact of interventions. Existing methods require extensive tuning of parameters that control the graph sparsity and temporal smoothness. Furthermore, these methods are computationally burdensome with time complexity $O(NP^3)$ for $P$ variables and $N$ time points. As a remedy, we propose a low-complexity tuning-free Bayesian approach, named BASS. Specifically, we impose temporally-dependent spike-and-slab priors on the graphs such that they are sparse and varying smoothly across time. A variational inference algorithm is then derived to learn the graph structures from the data automatically. Owning to the pseudo-likelihood and the mean-field approximation, the time complexity of BASS is only $O(NP^2)$. Additionally, by identifying the frequency-domain resemblance to the time-varying graphical models, we show that BASS can be extended to learning frequency-varying inverse spectral density matrices, and yields graphical models for multivariate stationary time series. Numerical results on both synthetic and real data show that that BASS can better recover the underlying true graphs, while being more efficient than the existing methods, especially for high-dimensional cases.