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Network Recovery from Unlabeled Noisy Samples

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.