Inference of Network Summary Statistics Through Network Denoising

TL;DR

This paper introduces a spectral-based denoising method for noisy network observations, improving the accuracy of network summary statistics inference by accounting for edge errors in a single observed network.

Contribution

The paper develops a novel spectral denoising approach that enhances the estimation of true network statistics from noisy observations, with theoretical performance bounds and practical demonstrations.

Findings

The denoising method improves accuracy of network summary statistics inference.

Theoretical bounds demonstrate the effectiveness of the spectral approach.

Practical results on synthetic and real data validate the methodology.

Abstract

Consider observing an undirected network that is `noisy' in the sense that there are Type I and Type II errors in the observation of edges. Such errors can arise, for example, in the context of inferring gene regulatory networks in genomics or functional connectivity networks in neuroscience. Given a single observed network then, to what extent are summary statistics for that network representative of their analogues for the true underlying network? Can we infer such statistics more accurately by taking into account the noise in the observed network edges? In this paper, we answer both of these questions. In particular, we develop a spectral-based methodology using the adjacency matrix to `denoise' the observed network data and produce more accurate inference of the summary statistics of the true network. We characterize performance of our methodology through bounds on appropriate notions of risk in the $L^2$ sense, and conclude by illustrating the practical impact of this work on synthetic and real-world data.