Domain-Invariant Component Analysis (DICA), a kernel-based optimization algorithm that learns an invariant transformation by minimizing the dissimilarity across domains, whilst preserving the functional relationship between input and output variables is proposed.Expand

This work considers domain adaptation under three possible scenarios, kernel embedding of conditional as well as marginal distributions, and proposes to estimate the weights or transformations by reweighting or transforming training data to reproduce the covariate distribution on the test domain.Expand

A comprehensive review of existing work and recent advances in the Hilbert space embedding of distributions, and to discuss the most challenging issues and open problems that could lead to new research directions.Expand

A kernel-based discriminative learning framework on probability measures that learns using a collection of probability distributions that have been constructed to meaningfully represent training data and proposes a flexible SVM (Flex-SVM) that places different kernel functions on each training example.Expand

This work poses causal inference as the problem of learning to classify probability distributions, and extends the ideas to infer causal relationships between more than two variables.Expand

It is shown that various types of VKDEs can be considered as solutions to a class of regularization problems studied in this paper, bridging the gap between large-margin methods and kernel density estimators.Expand

A new kernel CI test is proposed that uses a single, learned permutation to convert the CI test problem into an easier two-sample test problem and has power competitive with state-of-the-art kernel CI tests.Expand

Focusing on a subset of this class of estimators, this work proposes efficient shrinkage estimators for the kernel mean that can be improved due to a well-known phenomenon in statistics called Stein's phenomenon.Expand

A new operator-free, measure-theoretic definition of the conditional mean embedding as a random variable taking values in a reproducing kernel Hilbert space is presented, and a thorough analysis of its properties, including universal consistency is provided.Expand

The interesting aspect of this result is that the minimax rate is independent of the smoothness of the kernel and the density of $P$ (if it exists).Expand