Lydia Beaudrot | Searcharxiv

arXiv2026

Identifying common backbones of interactions underlying food webs via non-deterministic alignments

Climate change reshapes food webs by altering species distributions and interactions, making it essential to identify structural backbones of interactions that persist across ecosystems. Deterministic alignment methods are computationally slow and restricted to one-to-one correspondences. We introduce a scalable, non-deterministic alignment framework inspired by optimal transport that captures overlapping species roles via many-to-many mappings. Framed via motif-role profiles as a Gromov-Wasserstein transport problem, our method is both efficient and interpretable. We apply the proposed method to a large continental-scale data set of 129 mammal food webs in Sub-Saharan Africa. Pairwise alignments are identified, and we uncover robust backbones with greater connectivity and transitivity than those expected under null models. The proposed approach provides a formal, reproducible tool for forecasting ecosystem reorganization and conservation efforts.

q-bio.PE↗

arXiv2024

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.

stat.ML↗