A state-space approach to sparse dynamic network reconstruction

TL;DR

This paper introduces a state-space method combined with EM and Sparse Bayesian Learning to efficiently reconstruct sparse dynamic networks, reducing parameters and simplifying model selection.

Contribution

It presents a novel state-space approach that minimizes parameters and employs EM and SBL for improved network reconstruction and sparsity.

Findings

Reduces unknown parameters in network models

Uses EM algorithm to avoid gradient computation difficulties

Incorporates SBL for enhanced network sparsity

Abstract

Dynamic network reconstruction has been shown to be challenging due to the requirements on sparse network structures and network identifiability. The direct parametric method (e.g., using ARX models) requires a large amount of parameters in model selection. Amongst the parametric models, only a restricted class can easily be used to address network sparsity without rendering the optimization problem intractable. To overcome these problems, this paper presents a state-space-based method, which significantly reduces the number of unknown parameters in model selection. Furthermore, we avoid various difficulties arising in gradient computation by using the Expectation Minimization (EM) algorithm instead. To enhance network sparsity, the prior distribution is constructed by using the Sparse Bayesian Learning (SBL) approach in the M-step. To solve the SBL problem, another EM algorithm is embedded, where we impose conditions on network identifiability in each iteration. In a sum, this paper provides a solution to reconstruct dynamic networks that avoids the difficulties inherent to gradient computation and simplifies the model selection.