2022/10/12 by François Bachoc, Bachoc, François, Louis Béthune +5 · 2 citations
Computer Science · Engineering · Physics and Astronomy · #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Statistical Mechanics and Entropy #Water Systems and Optimization
paper · pdf · doi:10.48550/arxiv.2210.06574
openalex publication_date 2022/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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.