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We propose two novel nonparametric two-sample kernel tests based on the Maximum Mean Discrepancy (MMD). First, for a fixed kernel, we construct an MMD test using either permutations or a wild bootstrap, two popular numerical procedures to…
The ability to compute the exact divergence between two high-dimensional distributions is useful in many applications but doing so naively is intractable. Computing the alpha-beta divergence -- a family of divergences that includes the…
Accurate approximation of probability measures is essential in numerical applications. This paper explores the quantization of probability measures using the maximum mean discrepancy (MMD) distance as a guiding metric. We first investigate…
This article presents a general framework for the transport of probability measures towards minimum divergence generative modeling and sampling using ordinary differential equations (ODEs) and Reproducing Kernel Hilbert Spaces (RKHSs),…
We propose an improved estimator for the multi-task averaging problem, whose goal is the joint estimation of the means of multiple distributions using separate, independent data sets. The naive approach is to take the empirical mean of each…
Several researchers have proposed minimisation of maximum mean discrepancy (MMD) as a method to quantise probability measures, i.e., to approximate a target distribution by a representative point set. We consider sequential algorithms that…
Reasoning based on causality, instead of association has been considered as a key ingredient towards real machine intelligence. However, it is a challenging task to infer causal relationship/structure among variables. In recent years, an…
Model-free time-to-event regression under confounding presents challenges due to biases introduced by causal and censoring sampling mechanisms. This phenomenology poses problems for classical non-parametric estimators like Beran's or the…
We introduce two kernels that extend the mean map, which embeds probability measures in Hilbert spaces. The generative mean map kernel (GMMK) is a smooth similarity measure between probabilistic models. The latent mean map kernel (LMMK)…
We focus on the distribution regression problem: regressing to vector-valued outputs from probability measures. Many important machine learning and statistical tasks fit into this framework, including multi-instance learning and point…
Probabilistic forecasting is increasingly critical across high-stakes domains, from finance and epidemiology to climate science. However, current evaluation frameworks lack a consensus metric and suffer from two critical flaws: they often…
We propose a new, nonparametric approach to learning and representing transition dynamics in Markov decision processes (MDPs), which can be combined easily with dynamic programming methods for policy optimisation and value estimation. This…
Kernel methods are one of the cornerstones of learning-based control, modern system identification, surrogate modelling, and related fields. A key advantage of this class of learning and function approximation methods is the availability of…
This paper provides a unifying view of optimal kernel hypothesis testing across the MMD two-sample, HSIC independence, and KSD goodness-of-fit frameworks. Minimax optimal separation rates in the kernel and $L^2$ metrics are presented, with…
Efficient and scalable non-parametric or semi-parametric regression analysis and density estimation are of crucial importance to the fields of statistics and machine learning. However, available methods are limited in their ability to…
There exist some testing procedures based on the maximum mean discrepancy (MMD) to address the challenge of model specification. However, they ignore the presence of estimated parameters in the case of composite null hypotheses. In this…
We propose a new one-sample test for normality in a Reproducing Kernel Hilbert Space (RKHS). Namely, we test the null-hypothesis of belonging to a given family of Gaussian distributions. Hence our procedure may be applied either to test…
Most machine learning algorithms, such as classification or regression, treat the individual data point as the object of interest. Here we consider extending machine learning algorithms to operate on groups of data points. We suggest…
Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due…
In modern data analysis, nonparametric measures of discrepancies between random variables are particularly important. The subject is well-studied in the frequentist literature, while the development in the Bayesian setting is limited where…