Related papers: Kernel Two-Sample Hypothesis Testing Using Kernel …

We study two-sample variable selection: identifying variables that discriminate between the distributions of two sets of data vectors. Such variables help scientists understand the mechanisms behind dataset discrepancies. Although…

We propose a novel kernel-based nonparametric two-sample test, employing the combined use of kernel mean and kernel covariance embedding. Our test builds on recent results showing how such combined embeddings map distinct probability…

An accurate multiclass classification strategy is crucial to interpreting antibody tests. However, traditional methods based on confidence intervals or receiver operating characteristics lack clear extensions to settings with more than two…

Binary classification is a fundamental problem in machine learning. Recent development of quantum similarity-based binary classifiers and kernel method that exploit quantum interference and feature quantum Hilbert space opened up tremendous…

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…

Modern surveys have provided the astronomical community with a flood of high-dimensional data, but analyses of these data often occur after their projection to lower-dimensional spaces. In this work, we introduce a local two-sample…

Kernel-based tests provide a simple yet effective framework that use the theory of reproducing kernel Hilbert spaces to design non-parametric testing procedures. In this paper we propose new theoretical tools that can be used to study the…

We investigate a series of learning kernel problems with polynomial combinations of base kernels, which will help us solve regression and classification problems. We also perform some numerical experiments of polynomial kernels with…

We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, distances between…

We consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of…

We consider the problem of clustering a sample of probability distributions from a random distribution on $\mathbb R^p$. Our proposed partitioning method makes use of a symmetric, positive-definite kernel $k$ and its associated reproducing…

This expository article gives an overview of the theory of hypothesis testing of quantum states in finite dimensional Hilbert spaces. Optimal measurement strategy for testing binary quantum hypotheses, which result in minimum error…

Refining one's hypotheses in the light of data is a common scientific practice; however, the dependency on the data introduces selection bias and can lead to specious statistical analysis. An approach for addressing this is via conditioning…

Network (graph) data analysis is a popular research topic in statistics and machine learning. In application, one is frequently confronted with graph two-sample hypothesis testing where the goal is to test the difference between two graph…

Support vector machines (SVM) and other kernel techniques represent a family of powerful statistical classification methods with high accuracy and broad applicability. Because they use all or a significant portion of the training data,…

Despite their importance in supporting experimental conclusions, standard statistical tests are often inadequate for research areas, like the life sciences, where the typical sample size is small and the test assumptions difficult to…

Set classification problems arise when classification tasks are based on sets of observations as opposed to individual observations. In set classification, a classification rule is trained with $N$ sets of observations, where each set is…

Motivated by the increasing use of kernel-based metrics for high-dimensional and large-scale data, we study the asymptotic behavior of kernel two-sample tests when the dimension and sample sizes both diverge to infinity. We focus on the…

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…

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…