High-dimensional structure learning of sparse vector autoregressive models using fractional marginal pseudo-likelihood

TL;DR

This paper introduces PLVAR, a fast and accurate Bayesian method for learning sparse high-dimensional vector autoregressive models, outperforming penalized regression techniques in efficiency and accuracy.

Contribution

The paper proposes PLVAR, a novel Bayesian approach combining fractional marginal likelihood and pseudo-likelihood for efficient sparse VAR model learning.

Findings

PLVAR outperforms state-of-the-art penalized regression methods in speed and accuracy.

The method is proven to be consistent.

Demonstrated effective on both simulated and real-world datasets.

Abstract

Learning vector autoregressive models from multivariate time series is conventionally approached through least squares or maximum likelihood estimation. These methods typically assume a fully connected model which provides no direct insight to the model structure and may lead to highly noisy estimates of the parameters. Because of these limitations, there has been an increasing interest towards methods that produce sparse estimates through penalized regression. However, such methods are computationally intensive and may become prohibitively time-consuming when the number of variables in the model increases. In this paper we adopt an approximate Bayesian approach to the learning problem by combining fractional marginal likelihood and pseudo-likelihood. We propose a novel method, PLVAR, that is both faster and produces more accurate estimates than the state-of-the-art methods based on penalized regression. We prove the consistency of the PLVAR estimator and demonstrate the attractive performance of the method on both simulated and real-world data.