Robust reconstruction of sparse network dynamics

TL;DR

This paper introduces the Ergodic Basis Pursuit method for accurately reconstructing sparse network interactions from multivariate time series, leveraging statistical properties to ensure robustness and scalability.

Contribution

The paper presents a novel EBP method that guarantees exact sparse network reconstruction using statistical properties, scalable with network size and noise robustness.

Findings

Exact reconstruction when minimum time series length is met

Time series length scales quadratically with node degree

Method is robust against noise levels

Abstract

Reconstruction of the network interaction structure from multivariate time series is an important problem in multiple fields of science. This problem is ill-posed for large networks leading to the reconstruction of false interactions. We put forward the Ergodic Basis Pursuit (EBP) method that uses the network dynamics' statistical properties to ensure the exact reconstruction of sparse networks when a minimum length of time series is attained. We show that this minimum time series length scales quadratically with the node degree being probed and logarithmic with the network size. Our approach is robust against noise and allows us to treat the noise level as a parameter. We show the reconstruction power of the EBP in experimental multivariate time series from optoelectronic networks.