An Optimal Transport Approach for Network Regression
<|reference_start|>An Optimal Transport Approach for Network Regression: 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.<|reference_end|>
@article{zalles2024an,
    title={An Optimal Transport Approach for Network Regression},
    author={Alex G. Zalles, Kai M. Hung, Ann E. Finneran, Lydia Beaudrot, and
  C'esar A. Uribe},
    journal={arXiv preprint arXiv:2406.12204},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.12204},
    primaryClass={stat.ML cs.LG math.OC}
}