Related papers: Energy distance and kernel mean embedding for two …
The aim of the present work is a comparative study of different persistence kernels applied to various classification problems. After some necessary preliminaries on homology and persistence diagrams, we introduce five different kernels…
In this paper, we address the problem of two-sample testing in the presence of missing data under a variety of missingness mechanisms. Our focus is on the well-known energy distance-based two-sample test. In addition to the standard…
We consider the problem of two-sample testing in a semi-supervised setting with abundant unlabeled covariate data. Standard two-sample tests neglect covariate information, which has the potential to significantly boost performance. However,…
Energy distance is a statistical distance between the distributions of random variables, which characterizes the equality of the distributions. Utilizing the energy distance, we develop a nonparametric test for the diagonal symmetry, which…
The so-called 'energy test' is a frequentist technique used in experimental particle physics to decide whether two samples are drawn from the same distribution. Its usage requires a good understanding of the distribution of the test…
Representing, comparing, and measuring the distance between probability distributions is a key task in computational statistics and machine learning. The choice of representation and the associated distance determine properties of the…
Suppose two networks are observed for the same set of nodes, where each network is assumed to be generated from a weighted stochastic block model. This paper considers the problem of testing whether the community memberships of the two…
This document reviews the definition of the kernel distance, providing a gentle introduction tailored to a reader with background in theoretical computer science, but limited exposure to technology more common to machine learning,…
Given $M \geq 2$ distributions defined on a general measurable space, we introduce a nonparametric (kernel) measure of multi-sample dissimilarity (KMD) -- a parameter that quantifies the difference between the $M$ distributions. The…
In the context of kernel methods, the similarity between data points is encoded by the kernel function which is often defined thanks to the Euclidean distance, a common example being the squared exponential kernel. Recently, other distances…
Given $n$ observations from two balanced classes, consider the task of labeling an additional $m$ inputs that are known to all belong to \emph{one} of the two classes. Special cases of this problem are well-known: with complete knowledge of…
In this paper, we test whether two datasets share a common clustering structure. As a leading example, we focus on comparing clustering structures in two independent random samples from two mixtures of multivariate normal distributions.…
A new goodness-of-fit test for normality in high-dimension (and Reproducing Kernel Hilbert Space) is proposed. It shares common ideas with the Maximum Mean Discrepancy (MMD) it outperforms both in terms of computation time and applicability…
Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as a powerful discrepancy measure for probability distributions. The recent developments on…
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…
Equivalence testing, a fundamental problem in the field of distribution testing, seeks to infer if two unknown distributions on $[n]$ are the same or far apart in the total variation distance. Conditional sampling has emerged as a powerful…
This paper addresses the problem of filtering with a state-space model. Standard approaches for filtering assume that a probabilistic model for observations (i.e. the observation model) is given explicitly or at least parametrically. We…
Kernel methods are successful approaches for different machine learning problems. This success is mainly rooted in using feature maps and kernel matrices. Some methods rely on the eigenvalues/eigenvectors of the kernel matrix, while for…
Testing for the equality of two high-dimensional distributions is a challenging problem, and this becomes even more challenging when the sample size is small. Over the last few decades, several graph-based two-sample tests have been…
Kernel mean embeddings are a powerful tool to represent probability distributions over arbitrary spaces as single points in a Hilbert space. Yet, the cost of computing and storing such embeddings prohibits their direct use in large-scale…