Related papers: Some sharp performance bounds for least squares re…
Many regularization schemes for high-dimensional regression have been put forward. Most require the choice of a tuning parameter, using model selection criteria or cross-validation schemes. We show that a simple non-negative or…
There has been an explosion of interest in using $l_1$-regularization in place of $l_0$-regularization for feature selection. We present theoretical results showing that while $l_1$-penalized linear regression never outperforms…
For high-dimensional sparse parameter estimation problems, Log-Sum Penalty (LSP) regularization effectively reduces the sampling sizes in practice. However, it still lacks theoretical analysis to support the experience from previous…
Feature selection with specific multivariate performance measures is the key to the success of many applications, such as image retrieval and text classification. The existing feature selection methods are usually designed for…
We study a family of sparse estimators defined as minimizers of some empirical Lipschitz loss function -- which include the hinge loss, the logistic loss and the quantile regression loss -- with a convex, sparse or group-sparse…
In this paper, we study a fast approximation method for {\it large-scale high-dimensional} sparse least-squares regression problem by exploiting the Johnson-Lindenstrauss (JL) transforms, which embed a set of high-dimensional vectors into a…
In this paper, we consider a squared $L_1/L_2$ regularized model for sparse signal recovery from noisy measurements. We first establish the existence of optimal solutions to the model under mild conditions. Next, we propose a proximal…
Sparse logistic regression is for classification and feature selection simultaneously. Although many studies have been done to solve $\ell_1$-regularized logistic regression, there is no equivalently abundant work on solving sparse logistic…
Two important goals of high-dimensional modeling are prediction and variable selection. In this article, we consider regularization with combined $L_1$ and concave penalties, and study the sampling properties of the global optimum of the…
The recursive least-squares algorithm with $\ell_1$-norm regularization ($\ell_1$-RLS) exhibits excellent performance in terms of convergence rate and steady-state error in identification of sparse systems. Nevertheless few works have…
We study the problem of learning a sparse linear regression vector under additional conditions on the structure of its sparsity pattern. This problem is relevant in machine learning, statistics and signal processing. It is well known that a…
$L_1$ regularization is used for finding sparse solutions to an underdetermined linear system. As sparse signals are widely expected in remote sensing, this type of regularization scheme and its extensions have been widely employed in many…
The sparse linear reconstruction problem is a core problem in signal processing which aims to recover sparse solutions to linear systems. The original problem regularized by the total number of nonzero components (also known as $L_0$…
High-dimensional sparse modeling via regularization provides a powerful tool for analyzing large-scale data sets and obtaining meaningful, interpretable models. The use of nonconvex penalty functions shows advantage in selecting important…
In system identification, estimating parameters of a model using limited observations results in poor identifiability. To cope with this issue, we propose a new method to simultaneously select and estimate sensitive parameters as key model…
Feature selection is a standard approach to understanding and modeling high-dimensional classification data, but the corresponding statistical methods hinge on tuning parameters that are difficult to calibrate. In particular, existing…
In genetical genomics studies, it is important to jointly analyze gene expression data and genetic variants in exploring their associations with complex traits, where the dimensionality of gene expressions and genetic variants can both be…
We use transductive regression techniques to learn mappings between source and target features of given parallel corpora and use these mappings to generate machine translation outputs. We show the effectiveness of $L_1$ regularized…
Feature selection is one of the most decisive tools in understanding data and machine learning models. Among other methods, sparsity induced by $L^{1}$ penalty is one of the simplest and best studied approaches to this problem. Although…
We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…