Related papers: A fast and effective kernel two-sample test for la…
We propose a novel kernel-based two-sample test that leverages the spectral decomposition of the maximum mean discrepancy (MMD) statistic to identify and utilize well-estimated directional components in reproducing kernel Hilbert space…
We present a study of a kernel-based two-sample test statistic related to the Maximum Mean Discrepancy (MMD) in the manifold data setting, assuming that high-dimensional observations are close to a low-dimensional manifold. We characterize…
We propose a nonparametric two-sample test procedure based on Maximum Mean Discrepancy (MMD) for testing the hypothesis that two samples of functions have the same underlying distribution, using kernels defined on function spaces. This…
Nonparametric two sample testing deals with the question of consistently deciding if two distributions are different, given samples from both, without making any parametric assumptions about the form of the distributions. The current…
Kernel two-sample tests have been widely used for multivariate data to test equality of distributions. However, existing tests based on mapping distributions into a reproducing kernel Hilbert space mainly target specific alternatives and do…
Modern kernel-based two-sample tests have shown great success in distinguishing complex, high-dimensional distributions with appropriate learned kernels. Previous work has demonstrated that this kernel learning procedure succeeds, assuming…
Modern large-scale kernel-based tests such as maximum mean discrepancy (MMD) and kernelized Stein discrepancy (KSD) optimize kernel hyperparameters on a held-out sample via data splitting to obtain the most powerful test statistics. While…
We consider the variable selection problem for two-sample tests, aiming to select the most informative variables to determine whether two collections of samples follow the same distribution. To address this, we propose a novel framework…
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…
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…
We propose novel statistics which maximise the power of a two-sample test based on the Maximum Mean Discrepancy (MMD), by adapting over the set of kernels used in defining it. For finite sets, this reduces to combining (normalised) MMD…
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,…
We introduce a kernel-based two-sample test for comparing probability distributions up to group actions. Our construction yields invariant kernels for locally compact $\sigma$-compact groups and extends classical Haar-based approaches…
The kernel Maximum Mean Discrepancy~(MMD) is a popular multivariate distance metric between distributions that has found utility in two-sample testing. The usual kernel-MMD test statistic is a degenerate U-statistic under the null, and thus…
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…
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…
We propose a class of kernel-based two-sample tests, which aim to determine whether two sets of samples are drawn from the same distribution. Our tests are constructed from kernels parameterized by deep neural nets, trained to maximize test…
The paper introduces a new kernel-based Maximum Mean Discrepancy (MMD) statistic for measuring the distance between two distributions given finitely-many multivariate samples. When the distributions are locally low-dimensional, the proposed…
Two-sample and independence tests with the kernel-based MMD and HSIC have shown remarkable results on i.i.d. data and stationary random processes. However, these statistics are not directly applicable to non-stationary random processes, a…
Two-sample tests have been extensively employed in various scientific fields and machine learning such as evaluation on the effectiveness of drugs and A/B testing on different marketing strategies to discriminate whether two sets of samples…