Related papers: Revisiting Marginal Regression
We study the problem of high-dimensional variable selection via some two-step procedures. First we show that given some good initial estimator which is $\ell_{\infty}$-consistent but not necessarily variable selection consistent, we can…
We propose a new sparse regression method called the component lasso, based on a simple idea. The method uses the connected-components structure of the sample covariance matrix to split the problem into smaller ones. It then solves the…
Sparse linear regression methods such as Lasso require a tuning parameter that depends on the noise variance, which is typically unknown and difficult to estimate in practice. In the presence of heavy-tailed noise or adversarial outliers,…
In this paper, we propose a new method for estimation and constructing confidence intervals for low-dimensional components in a high-dimensional model. The proposed estimator, called Constrained Lasso (CLasso) estimator, is obtained by…
Previous work regarding low-rank matrix recovery has concentrated on the scenarios in which the matrix is noise-free and the measurements are corrupted by noise. However, in practical application, the matrix itself is usually perturbed by…
We propose a pivotal method for estimating high-dimensional sparse linear regression models, where the overall number of regressors $p$ is large, possibly much larger than $n$, but only $s$ regressors are significant. The method is a…
Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control…
We compute approximate solutions to L0 regularized linear regression using L1 regularization, also known as the Lasso, as an initialization step. Our algorithm, the Lass-0 ("Lass-zero"), uses a computationally efficient stepwise search to…
Regularized regression has become very popular nowadays, particularly on high-dimensional problems where the addition of a penalty term to the log-likelihood allows inference where traditional methods fail. A number of penalties have been…
This paper studies high-dimensional regression models with lasso when data is sampled under multi-way clustering. First, we establish convergence rates for the lasso and post-lasso estimators. Second, we propose a novel inference method…
This paper proposes a fast and accurate method for sparse regression in the presence of missing data. The underlying statistical model encapsulates the low-dimensional structure of the incomplete data matrix and the sparsity of the…
In this paper, we consider the classic measurement error regression scenario in which our independent, or design, variables are observed with several sources of additive noise. We will show that our motivating example's replicated…
It is well-known that the statistical performance of Lasso can suffer significantly when the covariates of interest have strong correlations. In particular, the prediction error of Lasso becomes much worse than computationally inefficient…
We propose the Bayesian adaptive Lasso (BaLasso) for variable selection and coefficient estimation in linear regression. The BaLasso is adaptive to the signal level by adopting different shrinkage for different coefficients. Furthermore, we…
Effect modification occurs when the effect of the treatment on an outcome varies according to the level of other covariates and often has important implications in decision making. When there are tens or hundreds of covariates, it becomes…
We consider the problem of estimating a low-dimensional parameter in high-dimensional linear regression. Constructing an approximately unbiased estimate of the parameter of interest is a crucial step towards performing statistical…
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…
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…
Beta regression is commonly employed when the outcome variable is a proportion. Since its conception, the approach has been widely used in applications spanning various scientific fields. A series of extensions have been proposed over time,…
We apply classical and Bayesian lasso regularizations to a family of models with the presence of mixture and process variables. We analyse the performance of these estimates with respect to ordinary least squares estimators by a simulation…