Related papers: Extended Comparisons of Best Subset Selection, For…
The popular Lasso approach for sparse estimation can be derived via marginalization of a joint density associated with a particular stochastic model. A different marginalization of the same probabilistic model leads to a different…
In life sciences, the experts generally use empirical knowledge to recode variables, choose interactions and perform selection by classical approach. The aim of this work is to perform automatic learning algorithm for variables selection…
Linear mixed models (LMMs) are instrumental for regression analysis with structured dependence, such as grouped, clustered, or multilevel data. However, selection among the covariates--while accounting for this structured…
For massive data sets, efficient computation commonly relies on distributed algorithms that store and process subsets of the data on different machines, minimizing communication costs. Our focus is on regression and classification problems…
We develop a fully automatic Bayesian Lasso via variational inference. This is a scalable procedure for approximating the posterior distribution. Special attention is driven to the knot selection in regression spline. In order to carry…
The Bayesian Lasso is constructed in the linear regression framework and applies the Gibbs sampling to estimate the regression parameters. This paper develops a new sparse learning model, named the Bayesian Lasso Sparse (BLS) model, that…
We consider the least-square linear regression problem with regularization by the $\ell^1$-norm, a problem usually referred to as the Lasso. In this paper, we first present a detailed asymptotic analysis of model consistency of the Lasso in…
We compare alternative computing strategies for solving the constrained lasso problem. As its name suggests, the constrained lasso extends the widely-used lasso to handle linear constraints, which allow the user to incorporate prior…
Shrinkage estimators that possess the ability to produce sparse solutions have become increasingly important to the analysis of today's complex datasets. Examples include the LASSO, the Elastic-Net and their adaptive counterparts.…
Recently, considerable interest has focused on variable selection methods in regression situations where the number of predictors, $p$, is large relative to the number of observations, $n$. Two commonly applied variable selection approaches…
The network Lasso is a recently proposed convex optimization method for machine learning from massive network structured datasets, i.e., big data over networks. It is a variant of the well-known least absolute shrinkage and selection…
Modern variable selection procedures make use of penalization methods to execute simultaneous model selection and estimation. A popular method is the LASSO (least absolute shrinkage and selection operator), the use of which requires…
We investigate the relation of two fundamental tools in machine learning and signal processing, that is the support vector machine (SVM) for classification, and the Lasso technique used in regression. We show that the resulting optimization…
Selective inference methods are developed for group lasso estimators for use with a wide class of distributions and loss functions. The method includes the use of exponential family distributions, as well as quasi-likelihood modeling for…
The identification of governing equations for dynamical systems is everlasting challenges for the fundamental research in science and engineering. Machine learning has exhibited great success to learn and predict dynamical systems from…
In the context of multiple regression model, suppose that the vector parameter of interest \beta is subjected to lie in the subspace hypothesis H\beta = h, where this restriction is based on either additional information or prior knowledge.…
We consider the problem of best subset selection (BSS) under high-dimensional sparse linear regression model. Recently, Guo et al. (2020) showed that the model selection performance of BSS depends on a certain identifiability margin, a…
We consider the least-square linear regression problem with regularization by the l1-norm, a problem usually referred to as the Lasso. In this paper, we present a detailed asymptotic analysis of model consistency of the Lasso. For various…
In high-dimensional statistics, variable selection recovers the latent sparse patterns from all possible covariate combinations. This paper proposes a novel optimization method to solve the exact L0-regularized regression problem, which is…
The Lasso has been widely used as a method for variable selection, valued for its simplicity and empirical performance. However, Lasso's selection stability deteriorates in the presence of correlated predictors. Several approaches have been…