Model Identification of a Network as Compressing Sensing

TL;DR

This paper introduces a method for identifying network models from time series data by estimating sparse Wiener filters, balancing accuracy and complexity, with applications demonstrated on real and simulated data.

Contribution

It presents a novel geometric and optimization framework for sparse network model identification without prior topology knowledge.

Findings

Effective in uncovering network structure from data

Balances model accuracy and sparsity

Validated on real and simulated datasets

Abstract

In many applications, it is important to derive information about the topology and the internal connections of dynamical systems interacting together. Examples can be found in fields as diverse as Economics, Neuroscience and Biochemistry. The paper deals with the problem of deriving a descriptive model of a network, collecting the node outputs as time series with no use of a priori insight on the topology, and unveiling an unknown structure as the estimate of a "sparse Wiener filter". A geometric interpretation of the problem in a pre-Hilbert space for wide-sense stochastic processes is provided. We cast the problem as the optimization of a cost function where a set of parameters are used to operate a trade-off between accuracy and complexity in the final model. The problem of reducing the complexity is addressed by fixing a certain degree of sparsity and finding the solution that "better" satisfies the constraints according to the criterion of approximation. Applications starting from real data and numerical simulations are provided.