Related papers: RAPTT: An Exact Two-Sample Test in High Dimensions…
This paper is devoted to the study of the general linear hypothesis testing (GLHT) problem of multi-sample high-dimensional mean vectors. For the GLHT problem, we introduce a test statistic based on $L^2$-norm and random integration method,…
Testing the equality of mean vectors across $g$ different groups plays an important role in many scientific fields. In regular frameworks, likelihood-based statistics under the normality assumption offer a general solution to this task.…
We propose a class of nonparametric two-sample tests with a cost linear in the sample size. Two tests are given, both based on an ensemble of distances between analytic functions representing each of the distributions. The first test uses…
Comparing two population means of network data is of paramount importance in a wide range of scientific applications. Many existing network inference solutions focus on global testing of entire networks, without comparing individual network…
Dimensionality reduction is a popular approach to tackle high-dimensional data with low-dimensional nature. Subspace Restricted Isometry Property, a newly-proposed concept, has proved to be a useful tool in analyzing the effect of…
In scientific and engineering scenarios, a recurring task is the detection of low-dimensional families of signals or patterns. A classic family of approaches, exemplified by template matching, aims to cover the search space with a dense…
t-SNE is a popular tool for embedding multi-dimensional datasets into two or three dimensions. However, it has a large computational cost, especially when the input data has many dimensions. Many use t-SNE to embed the output of a neural…
Large language models achieve state-of-the-art performance but are increasingly costly to fine-tune. Prompt tuning is a parameter-efficient fine-tuning method that addresses parameter-efficiency by learning prompt embeddings, but these…
In this era of large-scale data, distributed systems built on top of clusters of commodity hardware provide cheap and reliable storage and scalable processing of massive data. Here, we review recent work on developing and implementing…
The energy test is a powerful binning-free, multi-dimensional and distribution-free tool that can be applied to compare a measurement to a given prediction (goodness-of-fit) or to check whether two data samples originate from the same…
Genome-wide eQTL mapping explores the relationship between gene expression values and DNA variants to understand genetic causes of human disease. Due to the large number of genes and DNA variants that need to be assessed simultaneously,…
We consider the problem of testing the mean of high-dimensional data when the dimension may grow without explicit rate restrictions relative to the sample size. The proposed procedure is based on the statistic V_n = n||Xn||^2, which avoids…
Recent technical advances in collecting spatial data have been increasing the demand for methods to analyze large spatial datasets. The statistical analysis for these types of datasets can provide useful knowledge in various fields.…
The two-sample test is a fundamental problem in statistics with a wide range of applications. In the realm of high-dimensional data, nonparametric methods have gained prominence due to their flexibility and minimal distributional…
Matrix factorization is a simple and effective solution to the recommendation problem. It has been extensively employed in the industry and has attracted much attention from the academia. However, it is unclear what the low-dimensional…
Likelihood ratio tests are widely used to test statistical hypotheses about parametric families of probability distributions. If interest is restricted to a subfamily of distributions, then it is natural to inquire if the restricted LRT is…
We introduce a novel random projection technique for efficiently reducing the dimension of very high-dimensional tensors. Building upon classical results on Gaussian random projections and Johnson-Lindenstrauss transforms~(JLT), we propose…
Size distortion can occur if an asymptotic testing procedure requiring diverging sample sizes, is implemented to data with very small sample sizes. In this paper, we consider one-sample and two-sample tests for mean vectors when data are…
Dimensionality reduction techniques play important roles in the analysis of big data. Traditional dimensionality reduction approaches, such as principal component analysis (PCA) and linear discriminant analysis (LDA), have been studied…
We present a novel method for testing the hypothesis of equality of two correlation matrices using paired high-dimensional datasets. We consider test statistics based on the average of squares, maximum and sum of exceedances of Fisher…