Related papers: Nonparametric Linear Discriminant Analysis for Hig…

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…

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…

We propose a novel linear discriminant analysis approach for the classification of high-dimensional matrix-valued data that commonly arises from imaging studies. Motivated by the equivalence of the conventional linear discriminant analysis…

Statistical inference on histograms and frequency counts plays a central role in categorical data analysis. Moving beyond classical methods that directly analyze labeled frequencies, we introduce a framework that models the multiset of…

Researchers in the behavioral and social sciences use linear discriminant analysis (LDA) for predictions of group membership (classification) and for identifying the variables most relevant to group separation among a set of continuous…

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…

This paper derives the nonparametric maximum likelihood estimator (NPMLE) of a distribution function from observations which are subject to both bias and censoring. The NPMLE is obtained by a simple EM algorithm which is an extension of 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 the adoption of Artificial Intelligence (AI) models expands into critical real-world applications, ensuring the explainability of these models becomes paramount, particularly in sensitive fields such as medicine and finance. Linear…

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…

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.…

In this paper we study the computation of the nonparametric maximum likelihood estimator (NPMLE) in multivariate mixture models. Our first approach discretizes this infinite dimensional convex optimization problem by fixing the support…

A full parametric and linear specification may be insufficient to capture complicated patterns in studies exploring complex features, such as those investigating age-related changes in brain functional abilities. Alternatively, a partially…

A robust algorithm for non-negative matrix factorization (NMF) is presented in this paper with the purpose of dealing with large-scale data, where the separability assumption is satisfied. In particular, we modify the Linear Programming…

Evaluating the performance of large language models (LLMs) from human preference data is crucial for obtaining LLM leaderboards. However, many existing approaches either rely on restrictive parametric assumptions or lack valid uncertainty…

Probabilistic Linear Discriminant Analysis (PLDA) is a popular tool in open-set classification/verification tasks. However, the Gaussian assumption underlying PLDA prevents it from being applied to situations where the data is clearly…

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, different strands of literature are combined in order to obtain algorithms for semi-parametric estimation of discrete choice models that include the modelling of unobserved heterogeneity by using mixing distributions for the…