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Communication Dans Un Congrès Année : 2022

Gaussian Processes on Distributions based on Regularized Optimal Transport

Résumé

We present a novel kernel over the space of probability measures based on the dual formulation of optimal regularized transport. We propose an Hilbertian embedding of the space of probabilities using their Sinkhorn potentials, which are solutions of the dual entropic relaxed optimal transport between the probabilities and a reference measure $\mathcal{U}$. We prove that this construction enables to obtain a valid kernel, by using the Hilbert norms. We prove that the kernel enjoys theoretical properties such as universality and some invariances, while still being computationally feasible. Moreover we provide theoretical guarantees on the behaviour of a Gaussian process based on this kernel. The empirical performances are compared with other traditional choices of kernels for processes indexed on distributions.

Dates et versions

hal-03981114 , version 1 (09-02-2023)

Identifiants

Citer

François Bachoc, Louis Béthune, Alberto González-Sanz, Jean-Michel Loubes. Gaussian Processes on Distributions based on Regularized Optimal Transport. 26th International Conference on Artificial Intelligence and Statistics (AISTATS 2023), Apr 2023, Valencia, Spain. ⟨10.48550/arXiv.2210.06574⟩. ⟨hal-03981114⟩
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