Regularisation and central limit theorems for an inverse problem in network sampling applications

Abstract

An inverse problem motivated by packet sampling in communication networks and edge sampling in directed complex networks is studied through the operator perspective. The problem is shown to be ill-posed, with the resulting naive estimator potentially having very heavy tails, satisfying non-Gaussian central limit theorem and showing poor statistical performance. Regularisation of the problem leads to the Gaussian central limit theorem and superior performance of the regularised estimator, as a result of desirable properties of underlying operators. The limiting variance and convergence rates of the regularised estimator are also investigated. The results are illustrated on synthetic and real data from communication and complex networks.