The Variational Bayesian Inference for Network Autoregression Models

TL;DR

This paper introduces a variational Bayesian method for efficiently estimating large-scale dynamic network models, improving computational speed while maintaining accuracy, and effectively identifying network structures.

Contribution

It develops a novel variational Bayesian approach for dynamic network models, offering automatic structure detection and faster computation compared to MCMC methods.

Findings

VB approach detects various active network structures

Achieves similar or better accuracy than MCMC methods

Halves computational time in simulations and real data analysis

Abstract

We develop a variational Bayesian (VB) approach for estimating large-scale dynamic network models in the network autoregression framework. The VB approach allows for the automatic identification of the dynamic structure of such a model and obtains a direct approximation of the posterior density. Compared to Markov Chain Monte Carlo (MCMC) based sampling approaches, the VB approach achieves enhanced computational efficiency without sacrificing estimation accuracy. In the simulation study conducted here, the proposed VB approach detects various types of proper active structures for dynamic network models. Compared to the alternative approach, the proposed method achieves similar or better accuracy, and its computational time is halved. In a real data analysis scenario of day-ahead natural gas flow prediction in the German gas transmission network with 51 nodes between October 2013 and September 2015, the VB approach delivers promising forecasting accuracy along with clearly detected structures in terms of dynamic dependence.