Wasserstein barycenters are a fundamental tool for the analysis of distribution-valued data, but their computation and statistical analysis become challenging in high-dimensional and multi-sample settings. The unregularized barycenter problem is computationally demanding and suffers severely from the curse of dimension...
Peng-Tao Li, Alberto González-Sanz, Xiao-Hui Chen· 0 citations
This work provides the first theoretical explanation of mode collapse in MFVI and proposes RoVI, which augments MFVI with a rotation matrix, which augments MFVI with a rotation matrix.
Shunan Sheng, Bohan Wu, Alberto González-Sanz· arXiv.org· 1 citation
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 physics-informed flow matching as a motivating example. Satisfying a constraint more closely need not make the generated distribution more a...
Lea Kunkel, Alberto González-Sanz, Sophie Langer· 0 citations
We establish sharp convergence rates for quadratically regularized optimal transport with quadratic cost in the regime of small regularization $\varepsilon$. In particular, we quantify the sparsity of the support of the regularized optimizer. For smooth marginal densities in $\mathbb{R}^d$, this support lies within a d...
We study quadratically regularized optimal transport with quadratic cost in the regime of small regularization $\varepsilon$, where the support of the optimal coupling is sparse. For smooth marginal densities in $\mathbb{R}^d$, we show that the support contains the graph of the Brenier map. After centering by the Breni...
This work proposes a robust barycenter for distribution-valued data by incorporating the Huber loss directly into the optimal transport cost, and proves regularity and uniqueness properties of dual potentials, existence of optimal transport maps, and stability as the Huber parameter varies.
Carlos Cardoso-Perelló, Alberto González-Sanz· 0 citations
We establish sharp convergence rates for quadratically regularized optimal transport with quadratic cost in the regime of small regularization $\varepsilon$. In particular, we quantify the sparsity of the support of the regularized optimizer. For smooth marginal densities in $\mathbb{R}^d$, this support lies within a d...
Alberto González-Sanz, Marcel Nutz· 0 citations
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