Network Regression with Wasserstein Distances

Alexander Zalles, Kai M. Hung, Ann E. Finneran, Lydia Beaudrot, Cesar Uribe

Keywords: Regression, Networks, Wasserstein, Frobenius, Barycenter, Metrics

TL;DR: Network prediction with Wasserstein distances outperforms pre-existing methods in computational speed and accuracy.

Abstract: We study the problem of network regression, where the graph topology is inferred for unseen predictor values. We build upon recent developments on generalized regression models on metric spaces based on Fr\'echet 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. In the case of non-negative weights, 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 experiments. Additionally, real-world experiments utilizing the proposed approach result in larger metrics of model fitness, cementing improved prediction capabilities in practice.

Submission Number: 82