Related papers: Kernel Two-Sample Hypothesis Testing Using Kernel …
This paper is concerned with testing normality in a Hilbert space based on the maximum mean discrepancy. Specifically, we discuss the behavior of the test from two standpoints: asymptotics and practical aspects. Asymptotic normality of the…
Quantum one-class support vector machines leverage the advantage of quantum kernel methods for semi-supervised anomaly detection. However, their quadratic time complexity with respect to data size poses challenges when dealing with large…
When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…
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 a framework to construct practical kernel-based two-sample tests from the family of $f$-divergences. The test statistic is computed from the witness function of a regularized variational representation of the divergence, which we…
Representations of probability measures in reproducing kernel Hilbert spaces provide a flexible framework for fully nonparametric hypothesis tests of independence, which can capture any type of departure from independence, including…
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…
The Maximum Mean Discrepancy (MMD) has been the state-of-the-art nonparametric test for tackling the two-sample problem. Its statistic is given by the difference in expectations of the witness function, a real-valued function defined as a…
The two-sample problem, which consists in testing whether independent samples on $\mathbb{R}^d$ are drawn from the same (unknown) distribution, finds applications in many areas. Its study in high-dimension is the subject of much attention,…
Testing the equality of two conditional distributions is crucial in various modern applications, including transfer learning and causal inference. Despite its importance, this fundamental problem has received surprisingly little attention…
We consider the problem of distributed binary hypothesis testing of two sequences that are generated by an i.i.d. doubly-binary symmetric source. Each sequence is observed by a different terminal. The two hypotheses correspond to different…
Detecting the emergence of abrupt property changes in time series is a challenging problem. Kernel two-sample test has been studied for this task which makes fewer assumptions on the distributions than traditional parametric approaches.…
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…
Single-cell technologies offer insights into molecular feature distributions, but comparing them poses challenges. We propose a kernel-testing framework for non-linear cell-wise distribution comparison, analyzing gene expression and…
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…
The asymptotically optimal hypothesis testing problem with the general sources as the null and alternative hypotheses is studied under exponential-type error constraints on the first kind of error probability. Our fundamental philosophy in…
We characterize the asymptotic performance of nonparametric one- and two-sample testing. The exponential decay rate or error exponent of the type-II error probability is used as the asymptotic performance metric, and an optimal test…
Controlling false positives (Type I errors) through statistical hypothesis testing is a foundation of modern scientific data analysis. Existing causal structure discovery algorithms either do not provide Type I error control or cannot scale…
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…
In this article we study the field of Hilbertian metrics and positive definit (pd) kernels on probability measures, they have a real interest in kernel methods. Firstly we will make a study based on the Alpha-Beta-divergence to have a…