On Identification of Sparse Multivariable ARX Model: A Sparse Bayesian Learning Approach

TL;DR

This paper introduces a novel sparse Bayesian learning method for identifying multivariable ARX models, enabling the inference of network structure and dynamics directly from data without prior knowledge.

Contribution

It develops a new approach combining sparse Bayesian and group sparse Bayesian techniques for network identification in multivariable ARX models.

Findings

Effective inference of network structure and dynamics from data.

The proposed algorithm simplifies to re-weighted Sparse Group Lasso with known noise.

Applicable to systems biology and other fields for network inference.

Abstract

This paper begins with considering the identification of sparse linear time-invariant networks described by multivariable ARX models. Such models possess relatively simple structure thus used as a benchmark to promote further research. With identifiability of the network guaranteed, this paper presents an identification method that infers both the Boolean structure of the network and the internal dynamics between nodes. Identification is performed directly from data without any prior knowledge of the system, including its order. The proposed method solves the identification problem using Maximum a posteriori estimation (MAP) but with inseparable penalties for complexity, both in terms of element (order of nonzero connections) and group sparsity (network topology). Such an approach is widely applied in Compressive Sensing (CS) and known as Sparse Bayesian Learning (SBL). We then propose a novel scheme that combines sparse Bayesian and group sparse Bayesian to efficiently solve the problem. The resulted algorithm has a similar form of the standard Sparse Group Lasso (SGL) while with known noise variance, it simplifies to exact re-weighted SGL. The method and the developed toolbox can be applied to infer networks from a wide range of fields, including systems biology applications such as signaling and genetic regulatory networks.