Related papers: Generalized Kernel Two-Sample Tests
Two-sample hypothesis testing-determining whether two sets of data are drawn from the same distribution-is a fundamental problem in statistics and machine learning with broad scientific applications. In the context of nonparametric testing,…
This paper is about two related decision theoretic problems, nonparametric two-sample testing and independence testing. There is a belief that two recently proposed solutions, based on kernels and distances between pairs of points, behave…
Over the last decade, an approach that has gained a lot of popularity to tackle nonparametric testing problems on general (i.e., non-Euclidean) domains is based on the notion of reproducing kernel Hilbert space (RKHS) embedding of…
We present a general framework for hypothesis testing on distributions of sets of individual examples. Sets may represent many common data sources such as groups of observations in time series, collections of words in text or a batch of…
We propose a two-sample test for the means of high-dimensional data when the data dimension is much larger than the sample size. Hotelling's classical $T^2$ test does not work for this "large $p$, small $n$" situation. The proposed test…
Change-point analysis plays a significant role in various fields to reveal discrepancies in distribution in a sequence of observations. While a number of algorithms have been proposed for high-dimensional data, kernel-based methods have not…
In clinical and neuroscientific studies, systematic differences between two populations of brain networks are investigated in order to characterize mental diseases or processes. Those networks are usually represented as graphs built from…
This article concerns testing for equality of distribution between groups. We focus on screening variables with shared distributional features such as common support, modes and patterns of skewness. We propose a Bayesian testing method…
Reproducing Kernel Hilbert Space (RKHS) embedding of probability distributions has proved to be an effective approach, via MMD (maximum mean discrepancy), for nonparametric hypothesis testing problems involving distributions defined over…
Machine learning and deep learning have been used extensively to classify physical surfaces through images and time-series contact data. However, these methods rely on human expertise and entail the time-consuming processes of data and…
We propose a novel test procedure for comparing mean functions across two groups within the reproducing kernel Hilbert space (RKHS) framework. Our proposed method is adept at handling sparsely and irregularly sampled functional data when…
The kernel two-sample test based on the maximum mean discrepancy (MMD) is one of the most popular methods for detecting differences between two distributions over general metric spaces. In this paper we propose a method to boost the power…
We propose optimal Bayesian two-sample tests for testing equality of high-dimensional mean vectors and covariance matrices between two populations. In many applications including genomics and medical imaging, it is natural to assume that…
In the statistical literature, as well as in artificial intelligence and machine learning, measures of discrepancy between two probability distributions are largely used to develop measures of goodness-of-fit. We concentrate on quadratic…
In this paper, we study the problem of testing the mean vectors of high dimensional data in both one-sample and two-sample cases. The proposed testing procedures employ maximum-type statistics and the parametric bootstrap techniques to…
We provide a distribution-free test that can be used to determine whether any two joint distributions $p$ and $q$ are statistically different by inspection of a large enough set of samples. Following recent efforts from Long et al. [1], we…
We propose two nonparametric statistical tests of goodness of fit for conditional distributions: given a conditional probability density function $p(y|x)$ and a joint sample, decide whether the sample is drawn from $p(y|x)r_x(x)$ for some…
Graph-based tests are a class of non-parametric two-sample tests useful for analyzing high-dimensional data. The test statistics are constructed from similarity graphs (such as K-minimum spanning tree), and consequently, their performance…
Do two data samples come from different distributions? Recent studies of this fundamental problem focused on embedding probability distributions into sufficiently rich characteristic Reproducing Kernel Hilbert Spaces (RKHSs), to compare…
Distance-based tests, also called "energy statistics", are leading methods for two-sample and independence tests from the statistics community. Kernel-based tests, developed from "kernel mean embeddings", are leading methods for two-sample…