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Modeling and Topology Estimation of Low Rank Dynamical Networks

Wenqi Cao, Aming Li

TL;DR

This work establishes a necessary and sufficient condition that links the sparsity pattern of the filter to conditional Granger causality, and develops a consistent method for estimating all network edges.

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.

Modeling and Topology Estimation of Low Rank Dynamical Networks

TL;DR

This work establishes a necessary and sufficient condition that links the sparsity pattern of the filter to conditional Granger causality, and develops a consistent method for estimating all network edges.

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.

Paper Structure

This paper contains 11 sections, 61 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Low rank graphical model
  3. Linear Causal Dynamical Network
  4. Special Feedback Model
  5. Low Rank Dynamical Network
  6. Causal Wiener filter
  7. Topology learning by Wiener Filter
  8. Conditional Granger Causality
  9. LRDN Topology Learning
  10. Simulation Example
  11. Conclusions

Figures (1)

  • Figure 1: Graphs associated to different network models of the low rank process in the simulation example. Panel (a) also corresponds to the estimated LRDN graph by Theorem \ref{['thm:GrangerLDRN']}.