Related papers: Delaunay Weighted Two-sample Test for High-dimensi…

A common observation in data-driven applications is that high-dimensional data have a low intrinsic dimension, at least locally. In this work, we consider the problem of point estimation for manifold-valued data. Namely, given a finite set…

High-dimensional logistic regression is widely used in analyzing data with binary outcomes. In this paper, global testing and large-scale multiple testing for the regression coefficients are considered in both single- and two-regression…

The ratio between two probability density functions is an important component of various tasks, including selection bias correction, novelty detection and classification. Recently, several estimators of this ratio have been proposed. Most…

Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…

We present the results of a large number of simulation studies regarding the power of various non-parametric two-sample tests for multivariate data. This includes both continuous and discrete data. In general no single method can be relied…

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,…

For the task of relevance analysis, the conventional Tukey's test may be applied to the set of all pairwise comparisons. However, there were few studies that discuss both nonparametric k-sample comparisons and relevance analysis in high…

We consider linear regression problems with a varying number of random projections, where we provably exhibit a double descent curve for a fixed prediction problem, with a high-dimensional analysis based on random matrix theory. We first…

The estimation of surface integrals on the boundary of an unknown body is a challenge for nonparametric methods in statistics, with powerful applications to physics and image analysis, among other fields. Provided that one can determine…

High dimensional hypothesis test deals with models in which the number of parameters is significantly larger than the sample size. Existing literature develops a variety of individual tests. Some of them are sensitive to the dense and small…

We introduce a new method of performing high dimensional discriminant analysis, which we call multiDA. We achieve this by constructing a hybrid model that seamlessly integrates a multiclass diagonal discriminant analysis model and feature…

The standard paired-sample testing approach in the multidimensional setting applies multiple univariate tests on the individual features, followed by p-value adjustments. Such an approach suffers when the data carry numerous features. A…

Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional relationship between the dimension (say, $p$) and the sample size (say,…

An important class of two-sample multivariate homogeneity tests is based on identifying differences between the distributions of interpoint distances. While generating distances from point clouds offers a straightforward and intuitive way…

Due to the broad applications of elliptical models, there is a long line of research on goodness-of-fit tests for empirically validating them. However, the existing literature on this topic is generally confined to low-dimensional settings,…

Spatial association and heterogeneity are two critical areas in the research about spatial analysis, geography, statistics and so on. Though large amounts of outstanding methods has been proposed and studied, there are few of them tend to…

Studies on various facets of pattern classification is often imperative while working with multi-dimensional samples pertaining to diverse application scenarios. In this notion, weighted dimension-based distance measure has been one of the…

Given two distinct datasets, an important question is if they have arisen from the the same data generating function or alternatively how their data generating functions diverge from one another. In this paper, we introduce an approach for…

In this paper, we develop invariance-based procedures for testing and inference in high-dimensional regression models. These procedures, also known as randomization tests, provide several important advantages. First, for the global null…

We propose a two-sample test for high-dimensional means that requires neither distributional nor correlational assumptions, besides some weak conditions on the moments and tail properties of the elements in the random vectors. This…