An Optimal Transport Approach for Network Regression

• URL: http://arxiv.org/abs/2406.12204v1
• Date: Tue, 18 Jun 2024 02:03:07 GMT
• Title: An Optimal Transport Approach for Network Regression
• Authors: Alex G. Zalles, Kai M. Hung, Ann E. Finneran, Lydia Beaudrot, César A. Uribe,
• Abstract summary: We build upon recent developments in generalized regression models on metric spaces based on Fr'echet means. We propose a network regression method using the Wasserstein metric.
• Score: 0.6238182916866519
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the problem of network regression, where one is interested in how the topology of a network changes as a function of Euclidean covariates. We build upon recent developments in 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 network regression problem requires the computation of a Riemannian center of mass (i.e., Fr\'echet means). Fr\'echet means with non-negative weights translates into a barycenter problem and can be efficiently computed using fixed point iterations. Although the convergence guarantees of fixed-point iterations for the computation of Wasserstein affine averages remain an open problem, we provide evidence of convergence in a large number of synthetic and real-data scenarios. Extensive numerical results show that the proposed approach improves existing procedures by accurately accounting for graph size, topology, and sparsity in synthetic experiments. Additionally, real-world experiments using the proposed approach result in higher Coefficient of Determination ($R^{2}$) values and lower mean squared prediction error (MSPE), cementing improved prediction capabilities in practice.

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