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Two-sample tests for multivariate data and especially for non-Euclidean data are not well explored. This paper presents a novel test statistic based on a similarity graph constructed on the pooled observations from the two samples. It can…

Methodology · Statistics 2024-08-12 Hao Chen , Jerome H. Friedman

Estimating the location where an image was taken based solely on the contents of the image is a challenging task, even for humans, as properly labeling an image in such a fashion relies heavily on contextual information, and is not as…

Computer Vision and Pattern Recognition · Computer Science 2017-12-29 Jesse M. Johns , Jeremiah Rounds , Michael J. Henry

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…

Methodology · Statistics 2021-12-07 Kyoungjae Lee , Kisung You , Lizhen Lin

Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional condition on its rate of increase compared to the sample size. On the…

Statistics Theory · Mathematics 2024-03-26 Joydeep Chowdhury , Subhajit Dutta , Marc G. Genton

Sample weighting is widely used in deep learning. A large number of weighting methods essentially utilize the learning difficulty of training samples to calculate their weights. In this study, this scheme is called difficulty-based…

Machine Learning · Computer Science 2023-01-13 Xiaoling Zhou , Ou Wu , Weiyao Zhu , Ziyang Liang

In this paper, we propose a new scalar and shift transform invariant test statistic for the high-dimensional two-sample location test. The expectation of our test is exactly zero under the null hypothesis. And we allow the dimension could…

Methodology · Statistics 2015-02-20 Long Feng , Fasheng Sun

Data depth has been applied as a nonparametric measurement for ranking multivariate samples. In this paper, we focus on homogeneity tests to assess whether two multivariate samples are from the same distribution. There are many data…

Statistics Theory · Mathematics 2023-06-09 Yiting Chen , Wei Lin , Xiaoping Shi

In this paper, we develop a systematic theory for high dimensional analysis of variance in multivariate linear regression, where the dimension and the number of coefficients can both grow with the sample size. We propose a new \emph{U}~type…

Methodology · Statistics 2023-01-12 Zhipeng Lou , Xianyang Zhang , Wei Biao Wu

In many modern data sets, High dimension low sample size (HDLSS) data is prevalent in many fields of studies. There has been an increased focus recently on using machine learning and statistical methods to mine valuable information out of…

Optimization and Control · Mathematics 2023-05-23 Srivathsan Amruth , Xin Yee Lam

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…

Machine Learning · Statistics 2024-02-27 Xiuyuan Cheng , Yao Xie

Testing for the equality of two high-dimensional distributions is a challenging problem, and this becomes even more challenging when the sample size is small. Over the last few decades, several graph-based two-sample tests have been…

Methodology · Statistics 2019-11-22 Soham Sarkar , Rahul Biswas , Anil K. Ghosh

Dimensionless numbers and scaling laws provide elegant insights into the characteristic properties of physical systems. Classical dimensional analysis and similitude theory fail to identify a set of unique dimensionless numbers for a…

Fluid Dynamics · Physics 2022-12-28 Xiaoyu Xie , Wing Kam Liu , Zhengtao Gan

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…

Statistics Theory · Mathematics 2018-01-23 Jinyuan Chang , Chao Zheng , Wen-Xin Zhou , Wen Zhou

We consider the hypothesis testing problem of detecting a shift between the means of two multivariate normal distributions in the high-dimensional setting, allowing for the data dimension p to exceed the sample size n. Specifically, we…

Statistics Theory · Mathematics 2015-09-15 Miles E. Lopes , Laurent J. Jacob , Martin J. Wainwright

The hypothesis that high dimensional data tend to lie in the vicinity of a low dimensional manifold is the basis of manifold learning. The goal of this paper is to develop an algorithm (with accompanying complexity guarantees) for fitting a…

Statistics Theory · Mathematics 2013-12-23 Charles Fefferman , Sanjoy Mitter , Hariharan Narayanan

In this paper, we introduce an innovative testing procedure for assessing individual hypotheses in high-dimensional linear regression models with measurement errors. This method remains robust even when either the X-model or Y-model is…

Methodology · Statistics 2025-01-14 Shijie Cui , Xu Guo , Songshan Yang , Zhe Zhang

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,…

Statistics Theory · Mathematics 2023-02-09 Stephan Clémençon , Myrto Limnios , Nicolas Vayatis

This paper proposes a novel test method for high-dimensional mean testing regard for the temporal dependent data. Comparison to existing methods, we establish the asymptotic normality of the test statistic without relying on restrictive…

Methodology · Statistics 2025-12-01 Yuchen Hu , Xiaoyi Wang , Long Feng

High dimensional data analysis is known to be as a challenging problem. In this article, we give a theoretical analysis of high dimensional classification of Gaussian data which relies on a geometrical analysis of the error measure. It…

Statistics Theory · Mathematics 2008-07-10 Robin Girard

Precision matrix, which is the inverse of covariance matrix, plays an important role in statistics, as it captures the partial correlation between variables. Testing the equality of two precision matrices in high dimensional setting is a…

Methodology · Statistics 2018-10-23 Mingjuan Zhang , Yong He , Cheng Zhou , Xinsheng Zhang