Related papers: Nonparametric Mean and Variance Adaptive Classific…
This paper addresses classification problems with matrix-valued data, which commonly arise in applications such as neuroimaging and signal processing. Building on the assumption that the data from each class follows a matrix normal…
Linear discriminant analysis (LDA) is a typical method for classification problems with large dimensions and small samples. There are various types of LDA methods that are based on the different types of estimators for the covariance…
Discriminating patients with Alzheimer's disease (AD) from healthy subjects is a crucial task in the research of Alzheimer's disease. The task can be potentially achieved by linear discriminant analysis (LDA), which is one of the most…
Nonparametric empirical Bayes methods provide a flexible and attractive approach to high-dimensional data analysis. One particularly elegant empirical Bayes methodology, involving the Kiefer-Wolfowitz nonparametric maximum likelihood…
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…
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 propose a new learning method for heterogeneous domain adaptation (HDA), in which the data from the source domain and the target domain are represented by heterogeneous features with different dimensions. Using two different projection…
Despite its prevalence in statistical datasets, heteroscedasticity (non-constant sample variances) has been largely ignored in the high-dimensional statistics literature. Recently, studies have shown that the Lasso can accommodate…
Brittle optimization has been observed to adversely impact model likelihoods for regression and VAEs when simultaneously fitting neural network mappings from a (random) variable onto the mean and variance of a dependent Gaussian variable.…
Variable selection and classification are common objectives in the analysis of high-dimensional data. Most such methods make distributional assumptions that may not be compatible with the diverse families of distributions data can take. A…
Linear discriminant analysis (LDA) is a widely used technique for data classification. The method offers adequate performance in many classification problems, but it becomes inefficient when the data covariance matrix is ill-conditioned.…
We study mixture of linear regression (random coefficient) models, which capture population heterogeneity by allowing the regression coefficients to follow an unknown distribution $G^*$. In contrast to common parametric methods that fix the…
We study empirical Bayes estimation in high-dimensional linear regression. To facilitate computationally efficient estimation of the underlying prior, we adopt a variational empirical Bayes approach, introduced originally in Carbonetto and…
In this paper, we propose a new method to perform data augmentation in a reliable way in the High Dimensional Low Sample Size (HDLSS) setting using a geometry-based variational autoencoder. Our approach combines a proper latent space…
Heteroscedastic regression models a Gaussian variable's mean and variance as a function of covariates. Parametric methods that employ neural networks for these parameter maps can capture complex relationships in the data. Yet, optimizing…
This paper aims to develop an optimality theory for linear discriminant analysis in the high-dimensional setting. A data-driven and tuning free classification rule, which is based on an adaptive constrained $\ell_1$ minimization approach,…
We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the…
Classification is an important tool with many useful applications. Among the many classification methods, Fisher's Linear Discriminant Analysis (LDA) is a traditional model-based approach which makes use of the covariance information.…
As technology advanced, collecting data via automatic collection devices become popular, thus we commonly face data sets with lengthy variables, especially when these data sets are collected without specific research goals beforehand. It…
High-dimensional datasets are frequently subject to contamination by outliers and heavy-tailed noise, which can severely bias standard regularized estimators like the Lasso. While Maximum Mean Discrepancy (MMD) has recently been introduced…