Publications
Alberto González-Sanz, Marc Hallin and Bodhisattva Sen. Monotone Measure-Preserving Maps in Hilbert Spaces: Existence, Uniqueness, and Stability. Accepted in Bernoulli (2025). [arXiv]
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). [arXiv, 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). [arXiv, DOI]
Alberto González-Sanz and Marcel Nutz. Quantitative convergence of quadratically regularized linear programs. Applied Mathematics and Optimization 91(3): 1-18 (2024). [arXiv, 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). [arXiv, 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). [arXiv, 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). [arXiv, 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). [arXiv, JMLR]
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). [arXiv, DOI]
Eustasio del Barrio, Alberto González-Sanz and Jean-Michel Loubes. Central Limit Theorems for Semidiscrete Wasserstein Distances. Bernoulli 30(1): 554-580 (2024). [arXiv, 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). [arXiv, 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). [arXiv, 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). [arXiv, 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). [arXiv, 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. pp. 4986-5010 (2023). [arXiv, AISTATS]
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). [arXiv, NIPS]
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). [arXiv, DOI]
Serrurier, Mathieu, Franck Mamalet, Alberto González-Sanz, Thibaut Boissin, Jean-Michel Loubes and Eustasio del Barrio. Achieving robustness in classification using optimal transport with hinge regularization. Computer Vision and Pattern Recognition Conference. pp. 505-514 (2021). [arXiv, CVPR]
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. (2020). [arXiv, DOI]
Preprints
Alberto González-Sanz, Marc Hallin and Yisha Yao. Nonparametric Vector Quantile Autoregression. (2025) [arXiv]
Alberto González-Sanz, Eustasio del Barrio and Marcel Nutz. Sample Complexity of Quadratically Regularized Optimal Transport. (2025) [PDF]
Alberto González-Sanz, Marcel Nutz and Andrés Riveros Valdevenito. Linear Convergence of Gradient Descent for Quadratically Regularized Optimal Transport. (2025) [arXiv]
Alberto González-Sanz, Gilles Mordant, Álvaro Samperio and Bodhisattva Sen. Estimation of Algebraic Sets: Extending PCA Beyond Linearity. (2025) [arXiv]
Shunan Sheng, Bohan Wu, Alberto González-Sanz and Marcel Nutz. Stability of Mean-Field Variational Inference. (2025). [arXiv]
Eustasio del Barrio, Alberto González-Sanz, Jean-Michel Loubes and David Rodríguez-Vítores. Distributional Limit Theory for Optimal Transport. (2025). [arXiv]
Alberto González-Sanz, Stephan Eckstein and Marcel Nutz. Sparse Regularized Optimal Transport without Curse of Dimensionality. (2025). [arXiv]
François Bachoc, Alberto González-Sanz, Jean-Michel Loubes and Yisha Yao. Wasserstein Spatial Depth. (2024). [arXiv]
Marco Avella Medina and Alberto González-Sanz. On the breakdown point of transport-based quantiles. (2024). [arXiv]
Alberto González-Sanz and Marcel Nutz. Sparsity of Quadratically Regularized Optimal Transport: Scalar Case. (2024). [arXiv]
Alberto González-Sanz and Shunan Sheng. Linearization of Monge-Ampère equations and data science applications. (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. (2024). [arXiv]
Alberto González-Sanz and Shayan Hundrieser. Weak Limits for Empirical Entropic Optimal Transport: Beyond Smooth Costs. (2023). [arXiv]
Alberto González-Sanz, Jean-Michel Loubes and Jonathan Niles-Weed. Weak limits of entropy regularized Optimal Transport; potentials, plans and divergences. (2022). [arXiv]
Alberto González-Sanz, Lucas De Lara, Louis Béthune and Jean-Michel Loubes. GAN Estimation of Lipschitz Optimal Transport Maps. (2022). [arXiv]