Related papers: Subset Selection for Multiple Linear Regression vi…

A stochastic search method, the so-called Adaptive Subspace (AdaSub) method, is proposed for variable selection in high-dimensional linear regression models. The method aims at finding the best model with respect to a certain model…

Selectivity estimation aims at estimating the number of database objects that satisfy a selection criterion. Answering this problem accurately and efficiently is essential to many applications, such as density estimation, outlier detection,…

In this thesis we discuss machine learning methods performing automated variable selection for learning sparse predictive models. There are multiple reasons for promoting sparsity in the predictive models. By relying on a limited set of…

The coresets approach, also called subsampling or subset selection, aims to select a subsample as a surrogate for the observed sample and has found extensive applications in large-scale data analysis. Existing coresets methods construct the…

In big data analysis, a simple task such as linear regression can become very challenging as the variable dimension $p$ grows. As a result, variable screening is inevitable in many scientific studies. In recent years, randomized algorithms…

We consider the problem of matrix column subset selection, which selects a subset of columns from an input matrix such that the input can be well approximated by the span of the selected columns. Column subset selection has been applied to…

We typically construct optimal designs based on a single objective function. To better capture the breadth of an experiment's goals, we could instead construct a multiple objective optimal design based on multiple objective functions. While…

In regression with random design, we study the problem of selecting a model that performs well for out-of-sample prediction. We do not assume that any of the candidate models under consideration are correct. Our analysis is based on…

Forward regression is a statistical model selection and estimation procedure which inductively selects covariates that add predictive power into a working statistical regression model. Once a model is selected, unknown regression parameters…

The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…

Multiple matrix sampling is a survey methodology technique that randomly chooses a relatively small subset of items to be presented to survey respondents for the purpose of reducing respondent burden. The data produced are missing…

We consider the problem of online active learning to collect data for regression modeling. Specifically, we consider a decision maker with a limited experimentation budget who must efficiently learn an underlying linear population model.…

Feature selection is a critical step in the analysis of high-dimensional data, where the number of features often vastly exceeds the number of samples. Effective feature selection not only improves model performance and interpretability but…

Variable selection is central to high-dimensional data analysis, and various algorithms have been developed. Ideally, a variable selection algorithm shall be flexible, scalable, and with theoretical guarantee, yet most existing algorithms…

The era of huge data necessitates highly efficient machine learning algorithms. Many common machine learning algorithms, however, rely on computationally intensive subroutines that are prohibitively expensive on large datasets. Oftentimes,…

Multiobjective feature selection seeks to determine the most discriminative feature subset by simultaneously optimizing two conflicting objectives: minimizing the number of selected features and the classification error rate. The goal is to…

High-dimensional tests are applied to find relevant sets of variables and relevant models. If variables are selected by analyzing the sums of products matrices and a corresponding mean-value test is performed, there is the danger that the…

Model selection is an indispensable part of data analysis dealing very frequently with fitting and prediction purposes. In this paper, we tackle the problem of model selection in a general linear regression where the parameter matrix…

High-dimensional, low sample-size (HDLSS) data problems have been a topic of immense importance for the last couple of decades. There is a vast literature that proposed a wide variety of approaches to deal with this situation, among which…

Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time…