Estimating network edge probabilities by neighborhood smoothing

TL;DR

This paper introduces a neighborhood smoothing method for estimating network edge probabilities directly from adjacency matrices, offering a computationally efficient alternative to graphon estimation with strong practical performance.

Contribution

It proposes a novel neighborhood smoothing technique that avoids structural assumptions, improving link prediction accuracy and computational efficiency.

Findings

Outperforms benchmark methods in link prediction tasks

Achieves competitive mean-squared error rates

Requires minimal tuning for practical use

Abstract

The estimation of probabilities of network edges from the observed adjacency matrix has important applications to predicting missing links and network denoising. It has usually been addressed by estimating the graphon, a function that determines the matrix of edge probabilities, but this is ill-defined without strong assumptions on the network structure. Here we propose a novel computationally efficient method, based on neighborhood smoothing to estimate the expectation of the adjacency matrix directly, without making the structural assumptions that graphon estimation requires. The neighborhood smoothing method requires little tuning, has a competitive mean-squared error rate, and outperforms many benchmark methods on link prediction in simulated and real networks.