Eustasio del Barrio, Alberto González-Sanz, Jean-Michel Loubes, and David Rodríguez-Vítores.
Distributional Limit Theory for Optimal Transport.
Statistical Science, to appear (2026). Arxiv
Alberto González-Sanz, Michel Groppe, Axel Munk.
Identifiability and Exact Reconstruction of the
Optimal Transport Cost on Finite Spaces.
Discrete Applied Mathematics, to appear. (2026). Arxiv
Alberto González-Sanz and Shayan Hundrieser.
Weak Limits for Empirical Entropic Optimal
Transport: Beyond Smooth Costs.
Annals of Applied Probability, to appear. (2026). Arxiv
Alberto González-Sanz, Marcel Nutz, Andrés Riveros Valdevenito.
Polyak–Lojasiewicz Inequality for Quadratically Regularized Optimal Transport.
SIAM Journal on Optimization, to appear. (2026). Arxiv
Alberto González-Sanz and Marcel Nutz.
Sparsity of Quadratically Optimal Transport: Scalar Case.
SIAM Journal of Mathematical Analysis, 58(4): 4162-4183. (2026). DOI
Marco Avella Medina and Alberto González-Sanz.
On the breakdown point of transport-based quantiles.
Bernoulli, 32(3): 2501-2523. (2026) DOI
Alberto González-Sanz, Marc Hallin, and Bodhisattva Sen.
Monotone Measure-Preserving Maps in Hilbert Spaces:
Existence, Uniqueness, and Stability.
Bernoulli, 32(2): 1213-1242 (2026). DOI
François Bachoc, Louis Béthune, Alberto González-Sanz, and Jean-Michel Loubes.
Improved learning theory for kernel distribution regression
with two-stage sampling.
The Annals of Statistics, 53(4):1753–1782 (2025). DOI
Alberto González-Sanz, Marcel Nutz, and Andrés Riveros Valdevenito.
Monotonicity in Quadratically Regularized Linear Programs.
SIAM Journal on Optimization, 35(2):1419–1437 (2025). DOI
Alberto González-Sanz and Marcel Nutz.
Quantitative convergence of quadratically regularized linear programs.
Applied Mathematics and Optimization, 91(3):1–18 (2024). DOI
Lucas De Lara, Mathis Deronzier, Alberto González-Sanz, and Virgile Foy.
On the nonconvexity of some push-forward constraints
and its consequences in machine learning.
SIAM Journal on Mathematics of Data Science, 7(2):385–620 (2025). DOI
Alberto González-Sanz, Michel Groppe, and Axel Munk.
Nonlinear Inverse Optimal Transport: Identifiability of the
Transport Cost from its Marginals and Optimal Values.
SIAM Journal of Mathematical Analysis, 3(6):6963–8148 (2024). DOI
Eustasio del Barrio, Alberto Gonzalez-Sanz, and Marc Hallin.
Nonparametric Multiple-Output Center-Outward Quantile Regression.
Journal of the American Statistical Association, 1–15 (2024). DOI
Lucas de Lara, Alberto González-Sanz, Nicholas Asher, Laurent Risser, and Jean-Michel Loubes.
Transport-based Counterfactual Models.
Journal of Machine Learning Research, 25(136):1–59 (2024). DOI
Eustasio del Barrio and Alberto González-Sanz.
Regularity of center-outward distribution functions in non-convex domains.
Advanced Nonlinear Studies, 24(4):880–894 (2024). DOI
Eustasio del Barrio, Alberto González-Sanz, and Jean-Michel Loubes.
Central Limit Theorems for Semidiscrete Wasserstein Distances.
Bernoulli, 30(1):554–580 (2024). DOI
Eustasio del Barrio, Alberto González-Sanz, and Jean-Michel Loubes.
Central Limit Theorems for General Transportation Costs.
Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, 60(2):847–873 (2024). DOI
Javier González-Delgado, Alberto González-Sanz, Juan R. Cortés, and Pierre Neuvial.
Two-sample goodness-of-fit tests on the flat torus based on Wasserstein
distance and their relevance to structural biology.
Electronic Journal of Statistics, 17(1):1547–1586 (2023). DOI
Eustasio del Barrio, Alberto González-Sanz,
Jean-Michel Loubes, and Jonathan Niles-Weed.
An improved central limit theorem and fast convergence
rates for entropic transportation costs.
SIAM Journal on Mathematics of Data Science, 5(3):639–669 (2023). DOI
Lucas De Lara, Alberto González-Sanz, and Jean-Michel Loubes.
Diffeomorphic Registration using Sinkhorn Divergences.
SIAM Journal on Imaging Sciences, 16(1):250–279 (2023). DOI
François Bachoc, Louis Béthune, Alberto González-Sanz, and Jean-Michel Loubes.
Gaussian Processes on Distributions based on Regularized Optimal Transport.
Proceedings of the 26th International Conference on
Artificial Intelligence and Statistics. 4986–5010 (2023). Link
Laurent Risser, Alberto González-Sanz, Quentin Vincenot, and Jean-Michel Loubes.
Tackling Algorithmic Bias in Neural-Network Classifiers
using Wasserstein-2 Regularization.
Journal of Mathematical Imaging and Vision, 64(6):672–689 (2022). DOI
Louis Béthune, Thibaut Boissin, Mathieu Serrurier, Franck Mamalet,
Corentin Friedrich, and Alberto González-Sanz.
Pay attention to your loss: understanding misconceptions about
1-Lipschitz neural networks.
Advances in Neural Information Processing Systems. (2022). Link
Mathieu Serrurier, Franck Mamalet, Alberto González-Sanz, Thibaut Boissin,
Jean-Michel Loubes, and Eustasio del Barrio.
Achieving robustness in classification using optimal transport with hinge regularization.
Proceedings of the IEEE/CVF Conference on Computer Vision
and Pattern Recognition. 505–514. (2021). Link
Eustasio del Barrio, Alberto González-Sanz, and Marc Hallin.
A note on the regularity of optimal-transport-based center-outward
distribution and quantile functions.
Journal of Multivariate Analysis, 180:104678 (2020). DOI
Lea Kunkel, Alberto González-Sanz, and Sophie Langer.
When do explicit penalties improve flow matching?
Arxiv preprint. (2026). Arxiv
Alberto González-Sanz, Marcel Nutz.
Geometry and Convergence of Quadratically Regularized Optimal Transport II.
Arxiv preprint. (2026). Arxiv
Alberto González-Sanz, Marcel Nutz.
Geometry and Convergence of Quadratically Regularized Optimal Transport I.
Arxiv preprint (2026). Arxiv
Pengtao Li, Alberto González-Sanz, Xiaohui Chen.
Central limit theorems and bootstrap for sparse regularized multimarginal
optimal transport and barycenters.
Arxiv preprint. (2026). Arxiv
Carlos Cardoso-Perelló and Alberto González-Sanz.
Huber–Wasserstein barycenters for robust distribution-valued data.
Arxiv preprint (2026). Arxiv
Alberto González-Sanz, Gilles Mordant, and Shunan Sheng.
Empirical optimal transport potentials: fast rates and a functional central limit theorem.
Arxiv preprint (2026). Arxiv
Carlos Cardoso-Perelló, Alberto González-Sanz, and Marcel Nutz.
Sharp Asymptotics for Regularized Optimal Transport.
Arxiv preprint. (2026). Arxiv
Alberto González-Sanz, and Dimitri Konen.
Spatial depth characterizes probability measures.
Arxiv preprint. (2026). Arxiv
Alberto González-Sanz and Marcel Nutz.
Stability of Quadratically Regularized Optimal Transport.
Arxiv preprint. (2026). Arxiv
Alberto González-Sanz, Shunan Sheng, Bohan Wu and Marco Avella Medina.
The Influence Function of Transport-based Quantiles.
Arxiv preprint. (2026). Arxiv
Alberto González-Sanz, Rishabh S. Gvalani and Lukas Koch.
Sharp local sparsity of regularized optimal transport.
Arxiv preprint. (2026). Arxiv
Alberto González-Sanz and Marco Avella Medina.
Breakdown properties of optimal transport maps: general transportation costs.
Arxiv preprint. (2026). Arxiv
Shunan Sheng, Bohan Wu, Alberto González-Sanz.
Mode Collapse of Mean-Field Variational Inference.
Arxiv preprint. (2025). Arxiv
Alberto González-Sanz, Marc Hallin, and Yisha Yao.
Nonparametric Vector Quantile Autoregression.
Arxiv preprint. (2025). Arxiv
Alberto González-Sanz, Eustasio del Barrio and Marcel Nutz.
Sample Complexity of Quadratically Regularized Optimal Transport.
Arxiv preprint. (2025). Arxiv
Alberto González-Sanz, Marcel Nutz, and Andrés Riveros Valdevenito.
Linear Convergence of Gradient Descent for Quadratically Regularized Optimal Transport.
Arxiv preprint. (2025). Arxiv
Alberto González-Sanz, Gilles Mordant, Álvaro Samperio, and Bodhisattva Sen.
Estimation of Algebraic Sets: Extending PCA Beyond Linearity.
Arxiv preprint. (2025). Arxiv
Shunan Sheng, Bohan Wu, Alberto González-Sanz, and Marcel Nutz.
Stability of Mean-Field Variational Inference.
Arxiv preprint. (2025). Arxiv
Alberto González-Sanz, Stephan Eckstein, and Marcel Nutz.
Sparse Regularized Optimal Transport withoutCurse of Dimensionality.
Arxiv preprint. (2025). Arxiv
François Bachoc, Alberto González-Sanz, Jean-Michel Loubes, and Yisha Yao.
Wasserstein Spatial Depth.
Arxiv preprint. (2024). Arxiv
Alberto González-Sanz and Shunan Sheng.
Linearization of Monge-Ampère equations and data science applications.
Arxiv preprint. (2024). Arxiv
Alejandro Garriz-Molina, Alberto González-Sanz, and Gilles Mordant.
Infinitesimal behavior of Quadratically Regularized Optimal Transport and
its relation with the Porous Medium Equation.
Arxiv preprint. (2025). Arxiv
Alberto González-Sanz, Jean-Michel Loubes, and Jonathan Niles-Weed.
Weak limits of entropy regularized Optimal Transport; potentials, plans and divergences.
Arxiv preprint. (2022). Arxiv
Alberto González-Sanz, Lucas De Lara, Louis Béthune, and Jean-Michel Loubes.
GAN Estimation of Lipschitz Optimal Transport Maps.
Arxiv preprint. (2022). Arxiv