2023-04-11-bachoc23a.md

title	software	abstract	section	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
Gaussian Processes on Distributions based on Regularized Optimal Transport	https://anonymous.4open.science/r/SinkhornMuGP-D37E/README.md	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.	Regular Papers	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	bachoc23a	0	Gaussian Processes on Distributions based on Regularized Optimal Transport	4986	5010	4986-5010	4986	false	Bachoc, Fran\c{c}ois and B\'ethune, Louis and Gonzalez-Sanz, Alberto and Loubes, Jean-Michel	given family François Bachoc given family Louis Béthune given family Alberto Gonzalez-Sanz given family Jean-Michel Loubes	2023-04-11		Proceedings of The 26th International Conference on Artificial Intelligence and Statistics	206	inproceedings	date-parts 2023 4 11	https://proceedings.mlr.press/v206/bachoc23a/bachoc23a.pdf