Related papers: Optimal Feature Selection in High-Dimensional Disc…
Let $(Y,X_1,...,X_m)$ be a random vector. It is desired to predict $Y$ based on $(X_1,...,X_m)$. Examples of prediction methods are regression, classification using logistic regression or separating hyperplanes, and so on. We consider the…
The Lasso is one of the most important approaches for parameter estimation and variable selection in high dimensional linear regression. At the heart of its success is the attractive rate of convergence result even when $p$, the dimension…
In this paper, we address the challenging problem of selecting tuning parameters for high-dimensional sparse regression. We propose a simple and computationally efficient method, called path thresholding (PaTh), that transforms any tuning…
This paper proposes a convex formulation for sparse multicategory linear discriminant analysis and then extend it to the distributed setting when data are stored across multiple sites. The key observation is that for the purpose of…
Identifying the relevant variables for a classification model with correct confidence levels is a central but difficult task in high-dimension. Despite the core role of sparse logistic regression in statistics and machine learning, it still…
In recent years we have been able to gather large amounts of genomic data at a fast rate, creating situations where the number of variables greatly exceeds the number of observations. In these situations, most models that can handle a…
In variable selection, most existing screening methods focus on marginal effects and ignore dependence between covariates. To improve the performance of selection, we incorporate pairwise effects in covariates for screening and…
Most data sets comprise of measurements on continuous and categorical variables. In regression and classification Statistics literature, modeling high-dimensional mixed predictors has received limited attention. In this paper we study the…
We present the framework of slowly varying regression under sparsity, allowing sparse regression models to exhibit slow and sparse variations. The problem of parameter estimation is formulated as a mixed-integer optimization problem. We…
The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from…
Classification and probability estimation are fundamental tasks with broad applications across modern machine learning and data science, spanning fields such as biology, medicine, engineering, and computer science. Recent development of…
We propose a novel and computationally efficient approach for nonparametric conditional density estimation in high-dimensional settings that achieves dimension reduction without imposing restrictive distributional or functional form…
Quadratic discriminant analysis (QDA) is a standard tool for classification due to its simplicity and flexibility. Because the number of its parameters scales quadratically with the number of the variables, QDA is not practical, however,…
In high-dimensional regression modelling, the number of candidate covariates to be included in the predictor is quite large, and variable selection is crucial. In this work, we propose a new penalty able to guarantee both sparse variable…
For high-dimensional inference problems, statisticians have a number of competing interests. On the one hand, procedures should provide accurate estimation, reliable structure learning, and valid uncertainty quantification. On the other…
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…
A key obstacle in automated analytics and meta-learning is the inability to recognize when different datasets contain measurements of the same variable. Because provided attribute labels are often uninformative in practice, this task may be…
As the size of datasets used in statistical learning continues to grow, distributed training of models has attracted increasing attention. These methods partition the data and exploit parallelism to reduce memory and runtime, but suffer…
Sparse Ising problems can be found in application areas such as logistics, condensed matter physics and training of deep Boltzmann networks, but can be very difficult to tackle with high efficiency and accuracy. This report presents new…
Variable screening is a fast dimension reduction technique for assisting high dimensional feature selection. As a preselection method, it selects a moderate size subset of candidate variables for further refining via feature selection to…