Network Regression with Wasserstein Distances

Motivated by the explosion of graph-based data analysis, we study the problem of network regression, where graph topology is predicted for unseen predictor values. We build upon recent developments on generalized regression models on metric spaces based on Frèchet means and propose a network regression method using the Wasserstein metric. We show that when representing graphs as multivariate Gaussian distributions, the regression problem in the Wasserstein metric becomes a weighted Wasserstein barycenter problem. Such a weighted barycenter can be efficiently computed using fixed point iterations. Numerical results show that the proposed approach improves existing procedures by accurately accounting for graph size, randomness, and sparsity in synthetic and real-world experiments.