Estimating network edge probabilities by neighborhood smoothing
This addresses network analysis problems for researchers and practitioners working with incomplete or noisy network data, though it appears incremental relative to graphon-based approaches.
The authors tackled the problem of estimating network edge probabilities from observed adjacency matrices, which is important for link prediction and network denoising. Their neighborhood smoothing method achieved competitive mean-squared error rates and outperformed benchmark methods on simulated and real networks.
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.