4 citations · 9 across the 30 of their papers we have counts for
34 papers
When do explicit penalties improve flow matching?
Lea Kunkel, Alberto González-Sanz, Sophie Langer
Flow matching can learn structure directly from data, raising the question of when additional constraints improve generation. We study penalties that encode such constraints, with…
Geometry and Convergence of Quadratically Regularized Optimal Transport II
Alberto González-Sanz, Marcel Nutz
We study quadratically regularized optimal transport with quadratic cost in the regime of small regularization , where the support of the optimal coupling is sparse. F…
Geometry and Convergence of Quadratically Regularized Optimal Transport I
Alberto González-Sanz, Marcel Nutz
We establish sharp convergence rates for quadratically regularized optimal transport with quadratic cost in the regime of small regularization . In particular, we quan…
Central limit theorems and bootstrap for sparse regularized multimarginal optimal transport and barycenters
Pengtao Li, Alberto González-Sanz, Xiaohui Chen
Wasserstein barycenters are a fundamental tool for the analysis of distribution-valued data, but their computation and statistical analysis become challenging in high-dimensional a…
Huber-Wasserstein barycenters for robust distribution-valued data
Carlos Cardoso-Perelló, Alberto González-Sanz
We propose a robust barycenter for distribution-valued data by incorporating the Huber loss directly into the optimal transport cost. In contrast to metric-space Huber means, which…
Empirical optimal transport potentials: fast rates and a functional central limit theorem
Alberto González-Sanz, Gilles Mordant, Shunan Sheng
Optimal transport potentials are fundamental objects in statistics, economics, and machine learning: their gradients generate optimal transport maps, while the potentials themselve…
The Influence Function of Transport-based Quantiles
Alberto González-Sanz, Shunan Sheng, Bohan Wu +1
Transport-based quantiles extend univariate quantiles to multivariate distributions via optimal transport. We study the influence function of the transport quantile map $\mathbf{Q}…
Sharp Asymptotics for Regularized Optimal Transport
Carlos Cardoso-Perelló, Alberto González-Sanz, Marcel Nutz
We study the small-regularization limit for -regularized optimal transport with and for entropically regularized optimal transport (EOT). The exact first-order (r…
Finite-sample bounds for regularized optimal transport
Alberto González-Sanz, Marcel Nutz, Austin J. Stromme
We study the sample complexity of regularized optimal transport for general convex regularizations including the Kullback--Leibler divergence and penalties. Our main results…
Stability of Quadratically Regularized Optimal Transport
Alberto González-Sanz, Marcel Nutz
Quadratically regularized optimal transport (QOT) is a sparse alternative to entropic optimal transport. We develop a quantitative stability theory for QOT under perturbations of t…
Polyak-Lojasiewicz Inequality for Quadratically Regularized Optimal Transport
Alberto González-Sanz, Marcel Nutz, Andrés Riveros Valdevenito
Quadratically regularized optimal transport (QOT) is an alternative to entropic regularization that yields sparse couplings and avoids numerical instabilities due to exponential sc…
Breakdown properties of optimal transport maps: general transportation costs
Alberto Gonzalez-Sanz, Marco Avella Medina
Two recent works, Avella-Medina and González-Sanz (2026) and Passeggeri and Paindaveine (2026), studied the robustness of the optimal transport map through its breakdown point, i.e…
Sample Complexity of Quadratically Regularized Optimal Transport
Alberto González-Sanz, Eustasio del Barrio, Marcel Nutz
It is well known that optimal transport suffers from the curse of dimensionality: when the prescribed marginals are approximated by i.i.d. samples, the convergence of the empirical…
Mode Collapse of Mean-Field Variational Inference
Shunan Sheng, Bohan Wu, Alberto González-Sanz
Mean-field variational inference (MFVI) is a widely used method for approximating high-dimensional probability distributions by product measures. It has been empirically observed t…
Linear Convergence of Gradient Descent for Quadratically Regularized Optimal Transport
Alberto González-Sanz, Marcel Nutz, Andrés Riveros Valdevenito
In optimal transport, quadratic regularization is an alternative to entropic regularization when sparse couplings or small regularization parameters are desired. Quadratic regulari…
Estimation of Algebraic Sets: Extending PCA Beyond Linearity
Alberto González-Sanz, Gilles Mordant, Álvaro Samperio +1
An algebraic set is defined as the zero locus of a system of real polynomial equations. In this paper we address the problem of recovering an unknown algebraic set fr…
Stability of Mean-Field Variational Inference
Shunan Sheng, Bohan Wu, Alberto González-Sanz +1
Mean-field variational inference (MFVI) is a widely used method for approximating high-dimensional probability distributions by product measures. This paper studies the stability p…
Sparse Regularized Optimal Transport without Curse of Dimensionality
Alberto González-Sanz, Stephan Eckstein, Marcel Nutz
Entropic optimal transport -- the optimal transport problem regularized by KL diver\-gence -- is highly successful in statistical applications. Thanks to the smoothness of the entr…
Distributional Limit Theory for Optimal Transport
Eustasio del Barrio, Alberto González-Sanz, Jean-Michel Loubes +1
Optimal Transport (OT) is a resource allocation problem with applications in biology, data science, economics and statistics, among others. In some of the applications, practitione…
Identifiability and Exact Reconstruction of the Optimal Transport Cost on Finite Spaces
Alberto González-Sanz, Michel Groppe, Axel Munk
The goal of optimal transport (OT) is to find optimal assignments or matchings between data sets which minimize the total cost for a given cost function. However, sometimes the cos…
On the breakdown point of transport-based quantiles
Marco Avella-Medina, Alberto González-Sanz
Recent work has used optimal transport ideas to generalize the notion of (center-outward) quantiles to dimension . We study the robustness properties of these transport-ba…
Sparsity of Quadratically Regularized Optimal Transport: Scalar Case
Alberto González-Sanz, Marcel Nutz
The quadratically regularized optimal transport problem is empirically known to have sparse solutions: its optimal coupling has sparse support for small regulariz…
Monotonicity in Quadratically Regularized Linear Programs
Alberto González-Sanz, Marcel Nutz, Andrés Riveros Valdevenito
In optimal transport, quadratic regularization is a sparse alternative to entropic regularization: the solution measure tends to have small support. Computational experience sugges…
Linearization of Monge-Ampère Equations and Statistical Applications
Alberto González-Sanz, Shunan Sheng
Optimal transport has found numerous applications across data science, many of which require differentiating the optimal transport map with respect to the underlying probability de…