相关论文: Semiparametric Sparse Discriminant Analysis
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…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
We present a novel approach to the formulation and the resolution of sparse Linear Discriminant Analysis (LDA). Our proposal, is based on penalized Optimal Scoring. It has an exact equivalence with penalized LDA, contrary to the multi-class…
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…
Discriminant analysis, including linear discriminant analysis (LDA) and quadratic discriminant analysis (QDA), is a popular approach to classification problems. It is well known that LDA is suboptimal to analyze heteroscedastic data, for…
Dimensionality reduction is a crucial step for pattern recognition and data mining tasks to overcome the curse of dimensionality. Principal component analysis (PCA) is a traditional technique for unsupervised dimensionality reduction, which…
We propose a theoretical framework to analyze semi-supervised classification under the low density separation assumption in a high-dimensional regime. In particular, we introduce QLDS, a linear classification model, where the low density…
In this paper, we study randomized reduction methods, which reduce high-dimensional features into low-dimensional space by randomized methods (e.g., random projection, random hashing), for large-scale high-dimensional classification.…
Canonical correlation analysis investigates linear relationships between two sets of variables, but often works poorly on modern data sets due to high-dimensionality and mixed data types such as continuous, binary and zero-inflated. To…
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…
Semi-supervised learning is a model training method that uses both labeled and unlabeled data. This paper proposes a fully Bayes semi-supervised learning algorithm that can be applied to any multi-category classification problem. We assume…
Topological data analysis (TDA) has emerged as one of the most promising techniques to reconstruct the unknown shapes of high-dimensional spaces from observed data samples. TDA, thus, yields key shape descriptors in the form of persistent…
Ultra-high dimensional longitudinal data are increasingly common and the analysis is challenging both theoretically and methodologically. We offer a new automatic procedure for finding a sparse semivarying coefficient model, which is widely…
In this paper, we study the problem of high-dimensional sparse quadratic discriminant analysis (QDA). We propose a novel classification method, termed SSQDA, which is constructed via constrained convex optimization based on the sample…
The recent development of more sophisticated spectroscopic methods allows acqui- sition of high dimensional datasets from which valuable information may be extracted using multivariate statistical analyses, such as dimensionality reduction…
Parametric Bayesian modeling offers a powerful and flexible toolbox for machine learning. Yet the model, however detailed, may still be wrong, and this can make inferences untrustworthy. In this paper we introduce a new class of…
We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…
High-dimensional tensor-valued predictors arise in modern applications, increasingly as learned representations from neural networks. Existing tensor classification methods rely on sparsity or Tucker structures and often lack theoretical…
The performance of machine learning and pattern recognition algorithms generally depends on data representation. That is why, much of the current effort in performing machine learning algorithms goes into the design of preprocessing…
The most effective dimensionality reduction procedures produce interpretable features from the raw input space while also providing good performance for downstream supervised learning tasks. For many methods, this requires optimizing one or…