Robust Network Reconstruction in Polynomial Time

TL;DR

This paper introduces a polynomial-time algorithm for robustly reconstructing LTI system networks from noisy data, providing guarantees and a confidence measure for the selected structure.

Contribution

It offers a practical, efficient method with theoretical guarantees for network reconstruction under noise, improving robustness over previous approaches.

Findings

Algorithm tolerates higher noise levels than previous methods

Provides a set of candidate solutions spanning different sparsities

Includes a model-selection procedure with confidence measure

Abstract

This paper presents an efficient algorithm for robust network reconstruction of Linear Time-Invariant (LTI) systems in the presence of noise, estimation errors and unmodelled nonlinearities. The method here builds on previous work on robust reconstruction to provide a practical implementation with polynomial computational complexity. Following the same experimental protocol, the algorithm obtains a set of structurally-related candidate solutions spanning every level of sparsity. We prove the existence of a magnitude bound on the noise, which if satisfied, guarantees that one of these structures is the correct solution. A problem-specific model-selection procedure then selects a single solution from this set and provides a measure of confidence in that solution. Extensive simulations quantify the expected performance for different levels of noise and show that significantly more noise can be tolerated in comparison to the original method.