Network Recovery from Unlabeled Noisy Samples

TL;DR

This paper proposes a three-stage method to recover a parent network from noisy, unlabeled network samples, addressing a complex problem in statistical network analysis.

Contribution

It introduces a computationally feasible, asymptotically unbiased recovery procedure for unlabeled noisy networks, expanding the scope of network analysis methods.

Findings

The method effectively aligns networks via pairwise matching.

Sample averaging followed by thresholding estimates the parent network.

The approach is computationally tractable for complex network data.

Abstract

There is a growing literature on the statistical analysis of multiple networks in which the network is the fundamental data object. However, most of this work requires networks on a shared set of labeled vertices. In this work, we consider the question of recovering a parent network based on noisy unlabeled samples. We identify a specific regime in the noisy network literature for recovery that is asymptotically unbiased and computationally tractable based on a three-stage recovery procedure: first, we align the networks via a sequential pairwise graph matching procedure; next, we compute the sample average of the aligned networks; finally, we obtain an estimate of the parent by thresholding the sample average. Previous work on multiple unlabeled networks is only possible for trivial networks due to the complexity of brute-force computations.