Related papers: High-dimensional Linear Discriminant Analysis: Opt…
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…
We propose adaptive, line search-free second-order methods with optimal rate of convergence for solving convex-concave min-max problems. By means of an adaptive step size, our algorithms feature a simple update rule that requires solving…
This paper considers the problem of kernel regression and classification with possibly unobservable response variables in the data, where the mechanism that causes the absence of information is unknown and can depend on both predictors and…
This paper gives a theoretical analysis of high dimensional linear discrimination of Gaussian data. We study the excess risk of linear discriminant rules. We emphasis on the poor performances of standard procedures in the case when…
We study the distributional properties of the linear discriminant function under the assumption of normality by comparing two groups with the same covariance matrix but different mean vectors. A stochastic representation for the…
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
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…
In many social, economical, biological and medical studies, one objective is to classify a subject into one of several classes based on a set of variables observed from the subject. Because the probability distribution of the variables is…
High-dimensional data is common in multiple areas, such as health care and genomics, where the number of features can be tens of thousands. In such scenarios, the large number of features often leads to inefficient learning. Constraint…
In this work, we consider the algorithm to the (nonlinear) regression problems with $\ell_0$ penalty. The existing algorithms for $\ell_0$ based optimization problem are often carried out with a fixed step size, and the selection of an…
This paper proposes the capped least squares regression with an adaptive resistance parameter, hence the name, adaptive capped least squares regression. The key observation is, by taking the resistant parameter to be data dependent, the…
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…
In this study, we introduce an innovative methodology aimed at enhancing Fisher's Linear Discriminant Analysis (LDA) in the context of high-dimensional data classification scenarios, specifically addressing situations where each feature…
We propose novel randomized optimization methods for high-dimensional convex problems based on restrictions of variables to random subspaces. We consider oblivious and data-adaptive subspaces and study their approximation properties via…
In this paper, we study high-dimensional sparse Quadratic Discriminant Analysis (QDA) and aim to establish the optimal convergence rates for the classification error. Minimax lower bounds are established to demonstrate the necessity of…
Motivated by differential co-expression analysis in genomics, we consider in this paper estimation and testing of high-dimensional differential correlation matrices. An adaptive thresholding procedure is introduced and theoretical…
For high-dimensional classification, it is well known that naively performing the Fisher discriminant rule leads to poor results due to diverging spectra and noise accumulation. Therefore, researchers proposed independence rules to…
Linear discriminant analysis (LDA) is an important classification tool in statistics and machine learning. This paper investigates the varying coefficient LDA model for dynamic data, with Bayes' discriminant direction being a function of…
We develop a framework for analyzing the training and learning rate dynamics on a large class of high-dimensional optimization problems, which we call the high line, trained using one-pass stochastic gradient descent (SGD) with adaptive…
In large-scale, data-driven applications, parameters are often only known approximately due to noise and limited data samples. In this paper, we focus on high-dimensional optimization problems with linear constraints under uncertain…