# An Optimal Transport Approach for Network Regression

arXiv: https://arxiv.org/abs/2406.12204 · HTML: https://mlsanity.com/paper/2406.12204/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 41 references that are in the map.
- First posted on arXiv 18 Jun 2024.

## Builds on (most cited first, 16 of 16)

- [Machine Learning on Graphs: A Model and Comprehensive Taxonomy](https://mlsanity.com/paper/2005.03675/) (2020)
- [GOT: An Optimal Transport framework for Graph comparison](https://mlsanity.com/paper/1906.02085/) (2019)
- [Fr'echet Regression for Random Objects with Euclidean Predictors](https://mlsanity.com/paper/1608.03012/) (2016)
- [Entropy-Regularized 2-Wasserstein Distance between Gaussian Measures](https://mlsanity.com/paper/2006.03416/) (2020)
- [Fast Convergence Rates for Distributed Non-Bayesian Learning](https://mlsanity.com/paper/1508.05161/) (2015)
- [Learning to Predict Graphs with Fused Gromov-Wasserstein Barycenters](https://mlsanity.com/paper/2202.03813/) (2022)
- [On the Power of Edge Independent Graph Models](https://mlsanity.com/paper/2111.00048/) (2021)
- [Network Regression with Graph Laplacians](https://mlsanity.com/paper/2109.02981/) (2021)
- [Data-Driven Control of Complex Networks](https://mlsanity.com/paper/2003.12189/) (2020)
- [Wasserstein Regression with Empirical Measures and Density Estimation for Sparse Data](https://mlsanity.com/paper/2308.12540/) (2023)
- [Uniform convergence of local Fr'echet regression, with applications to locating extrema and time warping for metric space valued trajectories](https://mlsanity.com/paper/2006.13548/) (2020)
- [Conditional Wasserstein Barycenters and Interpolation/Extrapolation of Distributions](https://mlsanity.com/paper/2107.09218/) (2021)
- [FGOT: Graph Distances based on Filters and Optimal Transport](https://mlsanity.com/paper/2109.04442/) (2021)
- [Bures-Wasserstein Means of Graphs](https://mlsanity.com/paper/2305.19738/) (2023)
- [Exploring Human Mobility for Multi-Pattern Passenger Prediction: A Graph Learning Framework](https://mlsanity.com/paper/2202.10339/) (2022)
- [Barycenter Estimation of Positive Semi-Definite Matrices with Bures-Wasserstein Distance](https://mlsanity.com/paper/2302.14618/) (2023)

## Built on by (most cited first, 1 of 1)

- [Fr'echet Regression on the Bures-Wasserstein Manifold](https://mlsanity.com/paper/2604.03566/) (2026)

## Abstract (arXiv)

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 (R2) values and lower mean squared prediction error (MSPE), cementing improved prediction capabilities in practice.