Related papers: Safe preselection in lasso-type problems by cross-…
In spite of the wealth of literature on the theoretical properties of the Lasso, there is very little known when the value of the tuning parameter is chosen using the data, even though this is what actually happens in practice. We give a…
Sparse covariates are frequent in classification and regression problems and in these settings the task of variable selection is usually of interest. As it is well known, sparse statistical models correspond to situations where there are…
In high-dimensional survival analysis, effective variable selection is crucial for both model interpretation and predictive performance. This paper investigates Cox regression with lasso and adaptive lasso penalties in genomic datasets…
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…
Much theoretical and applied work has been devoted to high-dimensional regression with clean data. However, we often face corrupted data in many applications where missing data and measurement errors cannot be ignored. Loh and Wainwright…
We describe a fast method to eliminate features (variables) in l1 -penalized least-square regression (or LASSO) problems. The elimination of features leads to a potentially substantial reduction in running time, specially for large values…
High-dimensional variable selection, with many more covariates than observations, is widely documented in standard regression models, but there are still few tools to address it in non-linear mixed-effects models where data are collected…
The success of the Lasso in the era of high-dimensional data can be attributed to its conducting an implicit model selection, i.e., zeroing out regression coefficients that are not significant. By contrast, classical ridge regression can…
Penalized likelihood approaches are widely used for high-dimensional regression. Although many methods have been proposed and the associated theory is now well-developed, the relative efficacy of different approaches in finite-sample…
Causal effect estimation is a critical task in statistical learning that aims to find the causal effect on subjects by identifying causal links between a number of predictor (or, explanatory) variables and the outcome of a treatment. In a…
It is known that the Thresholded Lasso (TL), SCAD or MCP correct intrinsic estimation bias of the Lasso. In this paper we propose an alternative method of improving the Lasso for predictive models with general convex loss functions which…
Traditional variable selection methods could fail to be sign consistent when irrepresentable conditions are violated. This is especially critical in high-dimensional settings when the number of predictors exceeds the sample size. In this…
Ordered Weighted $L_{1}$ (OWL) regularized regression is a new regression analysis for high-dimensional sparse learning. Proximal gradient methods are used as standard approaches to solve OWL regression. However, it is still a burning issue…
Nowadays, l1 penalized likelihood has absorbed a high amount of consideration due to its simplicity and well developed theoretical properties. This method is known as a reliable method in order to apply in a broad range of applications…
Given data $y$ and $k$ covariates $x$ one problem in linear regression is to decide which in any of the covariates to include when regressing $y$ on the $x$. If $k$ is small it is possible to evaluate each subset of the $x$. If however $k$…
The $\ell_1$-penalized method, or the Lasso, has emerged as an important tool for the analysis of large data sets. Many important results have been obtained for the Lasso in linear regression which have led to a deeper understanding of…
The Lasso is a method for high-dimensional regression, which is now commonly used when the number of covariates $p$ is of the same order or larger than the number of observations $n$. Classical asymptotic normality theory does not apply to…
This paper studies macroeconomic forecasting and variable selection using a folded-concave penalized regression with a very large number of predictors. The penalized regression approach leads to sparse estimates of the regression…
We study a norm for structured sparsity which leads to sparse linear predictors whose supports are unions of prede ned overlapping groups of variables. We call the obtained formulation latent group Lasso, since it is based on applying the…
Lasso-type estimators are routinely used to estimate high-dimensional time series models. The theoretical guarantees established for these estimators typically require the penalty level to be chosen in a suitable fashion often depending on…