Estimating a network from multiple noisy realizations

TL;DR

This paper introduces a method to accurately estimate true networks from multiple noisy observations, especially in brain imaging, by leveraging community structures and providing theoretical guarantees for the estimates.

Contribution

It develops an efficient estimation technique for networks with community structure from noisy data, with proven convergence guarantees and practical validation.

Findings

Performance close to oracle methods on synthetic data

Stable and plausible brain network estimates from fMRI data

Effective noise level estimation in network reconstruction

Abstract

Complex interactions between entities are often represented as edges in a network. In practice, the network is often constructed from noisy measurements and inevitably contains some errors. In this paper we consider the problem of estimating a network from multiple noisy observations where edges of the original network are recorded with both false positives and false negatives. This problem is motivated by neuroimaging applications where brain networks of a group of patients with a particular brain condition could be viewed as noisy versions of an unobserved true network corresponding to the disease. The key to optimally leveraging these multiple observations is to take advantage of network structure, and here we focus on the case where the true network contains communities. Communities are common in real networks in general and in particular are believed to be presented in brain networks. Under a community structure assumption on the truth, we derive an efficient method to estimate the noise levels and the original network, with theoretical guarantees on the convergence of our estimates. We show on synthetic networks that the performance of our method is close to an oracle method using the true parameter values, and apply our method to fMRI brain data, demonstrating that it constructs stable and plausible estimates of the population network.