A Hilbert space embedding of a distribution—in short, a kernel mean embedding—has
recently emerged as a powerful tool for machine learning and statistical inference. The basic …

This paper is an attempt to bridge the conceptual gaps between researchers working on the
two widely used approaches based on positive definite kernels: Bayesian learning or …

" In this chapter, we introduce some of the very basics that are used throughout the book.
First, we give the definition of a topological space and related notions of open and closed …

Supervised operator learning is an emerging machine learning paradigm with applications
to modeling the evolution of spatio-temporal dynamical systems and approximating general …

We propose a framework for analyzing and comparing distributions, which we use to
construct statistical tests to determine if two samples are drawn from different distributions …

Abstract Domain adaptation arises in supervised learning when the training (source domain)
and test (target domain) data have different distributions. Let X and Y denote the features …

The random dot product graph (RDPG) is an independent-edge random graph that is
analytically tractable and, simultaneously, either encompasses or can successfully …

Let X denote the feature and Y the target. We consider domain adaptation under three
possible scenarios:(1) the marginal P_Y changes, while the conditional P_X| Y stays the …

We provide a unifying framework linking two classes of statistics used in two-sample and
independence testing: on the one hand, the energy distances and distance covariances …

We propose novel statistics which maximise the power of a two-sample test based on the
Maximum Mean Discrepancy (MMD), byadapting over the set of kernels used in defining it …