Modeling and Topology Estimation of Low Rank Dynamical Networks

TL;DR

This paper introduces a new low-rank dynamical network model that ensures identifiability and provides a consistent method for topology estimation using causal Wiener filtering, addressing limitations of existing methods.

Contribution

The paper proposes a novel low-rank dynamical network model with a theoretical condition linking filter sparsity to causality, enabling consistent topology estimation.

Findings

Simulation results show the method's accuracy and consistency.

The framework is parsimonious and effective for low-rank processes.

Theoretical link between filter sparsity and Granger causality is established.

Abstract

Conventional topology learning methods for dynamical networks become inapplicable to processes exhibiting low-rank characteristics. To address this, we propose the low rank dynamical network model which ensures identifiability. By employing causal Wiener filtering, we establish a necessary and sufficient condition that links the sparsity pattern of the filter to conditional Granger causality. Building on this theoretical result, we develop a consistent method for estimating all network edges. Simulation results demonstrate the parsimony of the proposed framework and consistency of the topology estimation approach.