Target Detection via Network Filtering

TL;DR

This paper introduces a network filtering method combining Lasso regression and residual analysis to detect external effects in large, sparse networks despite limited observations.

Contribution

It provides a formal characterization of detection accuracy in large sparse networks using a novel combination of Lasso and residual analysis.

Findings

Detection accuracy depends on network sparsity and topology.

Method performs well in simulated data scenarios.

Theoretical bounds are established for detection performance.

Abstract

A method of `network filtering' has been proposed recently to detect the effects of certain external perturbations on the interacting members in a network. However, with large networks, the goal of detection seems a priori difficult to achieve, especially since the number of observations available often is much smaller than the number of variables describing the effects of the underlying network. Under the assumption that the network possesses a certain sparsity property, we provide a formal characterization of the accuracy with which the external effects can be detected, using a network filtering system that combines Lasso regression in a sparse simultaneous equation model with simple residual analysis. We explore the implications of the technical conditions underlying our characterization, in the context of various network topologies, and we illustrate our method using simulated data.