2021/02/05 by Anton Mallasto, Mallasto, Anton
Computer Science · Mathematics · #Applied mathematics #Divergence (linguistics) #FOS: Computer and information sciences #Gaussian #Gaussian Processes and Bayesian Inference #Linguistics #Machine Learning (cs.LG) #Mathematics #Philosophy #Physics #Pure mathematics #Statistical Methods and Inference #Statistical and numerical algorithms #cs.LG
paper · pdf · doi:10.48550/arxiv.2102.03267
arxiv created 2021/02/05 · openalex publication_date 2021/02/05 · arxiv updated 2021/02/08 · openalex created_date 2021/02/15 · openalex updated_date 2026/07/28
Optimal Transport (OT) has emerged as an important computational tool in machine learning and computer vision, providing a geometrical framework for studying probability measures. OT unfortunately suffers from the curse of dimensionality and requires regularization for practical computations, of which the entropic regularization is a popular choice, which can be 'unbiased', resulting in a Sinkhorn divergence. In this work, we study the convergence of estimating the 2-Sinkhorn divergence between Gaussian processes (GPs) using their finite-dimensional marginal distributions. We show almost sure convergence of the divergence when the marginals are sampled according to some base measure. Furthermore, we show that using n marginals the estimation error of the divergence scales in a dimension-free way as O(ε^ -1n-(1)/(2)), where ε is the magnitude of entropic regularization.