Sparse Bayesian Inference of Multivariable ARX Networks

TL;DR

This paper introduces GESBL, a novel data-driven Bayesian method for inferring sparse multivariable ARX networks that automatically balances network sparsity and model complexity without tuning.

Contribution

The paper presents GESBL, a new Bayesian inference approach combining SBL and GSBL to automatically penalize network complexity and sparsity in multivariable ARX models.

Findings

GESBL outperforms existing methods on synthetic data

It effectively infers sparse networks with minimal tuning

Applicable to biological and power systems

Abstract

Increasing attention has recently been given to the inference of sparse networks. In biology, for example, most molecules only bind to a small number of other molecules, leading to sparse molecular interaction networks. To achieve sparseness, a common approach consists of applying weighted penalties to the number of links between nodes in the network and the complexity of the dynamics of existing links. The selection of proper weights, however, is non-trivial. Alternatively, this paper proposes a novel data-driven method, called GESBL, that is able to penalise both network sparsity and model complexity without any tuning. GESBL combines Sparse Bayesian Learning (SBL) and Group Sparse Bayesian Learning (GSBL) to introduce penalties for complexity, both in terms of element (system order of nonzero connections) and group sparsity (network topology). The paper considers a class of sparse linear time-invariant networks where the dynamics are represented by multivariable ARX models. Data generated from sparse random ARX networks and synthetic gene regulatory networks indicate that our method, on average, considerably outperforms existing state-of-the-art methods. The proposed method can be applied to a wide range of fields, from systems biology applications in signalling and genetic regulatory networks to power systems.