Related papers: Quantile regression: a penalization approach

Variable selection and dimension reduction are two commonly adopted approaches for high-dimensional data analysis, but have traditionally been treated separately. Here we propose an integrated approach, called sparse gradient learning…

We study sparse linear regression over a network of agents, modeled as an undirected graph (with no centralized node). The estimation problem is formulated as the minimization of the sum of the local LASSO loss functions plus a quadratic…

Mixtures of matrix Gaussian distributions provide a probabilistic framework for clustering continuous matrix-variate data, which are becoming increasingly prevalent in various fields. Despite its widespread adoption and successful…

We consider the group lasso penalty for the linear model. We note that the standard algorithm for solving the problem assumes that the model matrices in each group are orthonormal. Here we consider a more general penalty that blends the…

Classification with a sparsity constraint on the solution plays a central role in many high dimensional machine learning applications. In some cases, the features can be grouped together so that entire subsets of features can be selected or…

Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is done by solving an l_1-regularized linear regression problem, usually called Lasso. In this work we first combine the…

We propose a new method for supervised learning, especially suited to wide data where the number of features is much greater than the number of observations. The method combines the lasso ($\ell_1$) sparsity penalty with a quadratic penalty…

In this paper, the fused graphical lasso (FGL) method is used to estimate multiple precision matrices from multiple populations simultaneously. The lasso penalty in the FGL model is a restraint on sparsity of precision matrices, and a…

While K-means is known to be a standard clustering algorithm, its performance may be compromised due to the presence of outliers and high-dimensional noisy variables. This paper proposes adaptively robust and sparse K-means clustering…

Using a multiplicative reparametrization, I show that a subclass of $L_q$ penalties with $q\leq 1$ can be expressed as sums of $L_2$ penalties. It follows that the lasso and other norm-penalized regression estimates may be obtained using a…

Grouping structures arise naturally in many statistical modeling problems. Several methods have been proposed for variable selection that respect grouping structure in variables. Examples include the group LASSO and several concave group…

We study the performance of sparse regression methods and propose new techniques to distill the governing equations of dynamical systems from data. We first look at the generic methodology of learning interpretable equation forms from data,…

We consider the problem of sparse variable selection in nonparametric additive models, with the prior knowledge of the structure among the covariates to encourage those variables within a group to be selected jointly. Previous works either…

In real-world application scenarios, the identification of groups poses a significant challenge due to possibly occurring outliers and existing noise variables. Therefore, there is a need for a clustering method which is capable of…

Sparse linear regression -- finding an unknown vector from linear measurements -- is now known to be possible with fewer samples than variables, via methods like the LASSO. We consider the multiple sparse linear regression problem, where…

We propose a new fast algorithm to estimate any sparse generalized linear model with convex or non-convex separable penalties. Our algorithm is able to solve problems with millions of samples and features in seconds, by relying on…

Varying coefficient regression is a flexible technique for modeling data where the coefficients are functions of some effect-modifying parameter, often time or location in a certain domain. While there are a number of methods for variable…

Sparse regression and classification estimators that respect group structures have application to an assortment of statistical and machine learning problems, from multitask learning to sparse additive modeling to hierarchical selection.…

By treating intervals as inseparable sets, this paper proposes sparse machine learning regressions for high-dimensional interval-valued time series. With LASSO or adaptive LASSO techniques, we develop a penalized minimum distance…

In this manuscript, a new high-dimensional approach for simultaneous variable and group selection is proposed, called sparse-group SLOPE (SGS). SGS achieves false discovery rate control at both variable and group levels by incorporating the…