Related papers: On Two Simple and Effective Procedures for High Di…

In high-dimensional classification problems, a commonly used approach is to first project the high-dimensional features into a lower dimensional space, and base the classification on the resulting lower dimensional projections. In this…

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…

Reduced-rank linear discriminant analysis (RRLDA) is a foundational method of dimension reduction for classification that has been useful in a wide range of applications. The goal is to identify an optimal subspace to project the…

Gini distance correlation (GDC) was recently proposed to measure the dependence between a categorical variable, Y, and a numerical random vector, X. It mutually characterizes independence between X and Y. In this article, we utilize the GDC…

The degree to which subjects differ from each other with respect to certain properties measured by a set of variables, plays an important role in many statistical methods. For example, classification, clustering, and data visualization…

Categorical variables are of uttermost importance in biomedical research. When two of them are considered, it is often the case that one wants to test whether or not they are statistically dependent. We show weaknesses of classical methods…

Although being a crucial question for the development of machine learning algorithms, there is still no consensus on how to compare classifiers over multiple data sets with respect to several criteria. Every comparison framework is…

We propose a modification of linear discriminant analysis, referred to as compressive regularized discriminant analysis (CRDA), for analysis of high-dimensional datasets. CRDA is specially designed for feature elimination purpose and can be…

Ranking or assessing centrality in multivariate and non-Euclidean data is difficult because there is no canonical order and many depth notions become computationally fragile in high-dimensional or structured settings. We introduce a…

A good classification method should yield more accurate results than simple heuristics. But there are classification problems, especially high-dimensional ones like the ones based on image/video data, for which simple heuristics can work…

In high dimension, low sample size (HDLSS)settings, the simple average distance classifier based on the Euclidean distance performs poorly if differences between the locations get masked by the scale differences. To rectify this issue,…

Statisticians increasingly face the problem to reconsider the adaptability of classical inference techniques. In particular, divers types of high-dimensional data structures are observed in various research areas; disclosing the boundaries…

In this work we show that the classification performance of high-dimensional structural MRI data with only a small set of training examples is improved by the usage of dimension reduction methods. We assessed two different dimension…

Finding statistically significant interactions between binary variables is computationally and statistically challenging in high-dimensional settings, due to the combinatorial explosion in the number of hypotheses. Terada et al. recently…

This thesis responds to the challenges of using a large number, such as thousands, of features in regression and classification problems. There are two situations where such high dimensional features arise. One is when high dimensional…

Given a random sample from a multivariate population, estimating the number of large eigenvalues of the population covariance matrix is an important problem in Statistics with wide applications in many areas. In the context of Principal…

This article carries out a large dimensional analysis of standard regularized discriminant analysis classifiers designed on the assumption that data arise from a Gaussian mixture model with different means and covariances. The analysis…

We propose novel methodology for testing equality of model parameters between two high-dimensional populations. The technique is very general and applicable to a wide range of models. The method is based on sample splitting: the data is…

We consider the high-dimensional discriminant analysis problem. For this problem, different methods have been proposed and justified by establishing exact convergence rates for the classification risk, as well as the l2 convergence results…

Huge amount of applications in various fields, such as gene expression analysis or computer vision, undergo data sets with high-dimensional low-sample-size (HDLSS), which has putted forward great challenges for standard statistical and…