Related papers: Bolasso: model consistent Lasso estimation through…
Meinshausen and Buhlmann [Ann. Statist. 34 (2006) 1436--1462] showed that, for neighborhood selection in Gaussian graphical models, under a neighborhood stability condition, the LASSO is consistent, even when the number of variables is of…
Popular regularizers with non-differentiable penalties, such as Lasso, Elastic Net, Generalized Lasso, or SLOPE, reduce the dimension of the parameter space by inducing sparsity or clustering in the estimators' coordinates. In this paper,…
The problems of Lasso regression and optimal design of experiments share a critical property: their optimal solutions are typically \emph{sparse}, i.e., only a small fraction of the optimal variables are non-zero. Therefore, the…
We propose a generalized debiased Lasso estimator based on a stability principle. When a single column of the design matrix is perturbed, the estimator admits a simple update formula that can be computed from the original solution. Under…
Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…
We consider the fundamental problem of estimating the mean of a vector $y=X\beta+z$, where $X$ is an $n\times p$ design matrix in which one can have far more variables than observations, and $z$ is a stochastic error term--the so-called…
Variable selection is one of the most important tasks in statistics and machine learning. To incorporate more prior information about the regression coefficients, the constrained Lasso model has been proposed in the literature. In this…
We consider the problem of fitting the parameters of a high-dimensional linear regression model. In the regime where the number of parameters $p$ is comparable to or exceeds the sample size $n$, a successful approach uses an…
Bootstrap techniques (also called resampling computation techniques) have introduced new advances in modeling and model evaluation. Using resampling methods to construct a series of new samples which are based on the original data set,…
A sparse modeling is a major topic in machine learning and statistics. LASSO (Least Absolute Shrinkage and Selection Operator) is a popular sparse modeling method while it has been known to yield unexpected large bias especially at a sparse…
Stroke remains a leading cause of death and disability worldwide, yet effective prediction of stroke risk using large-scale population data remains challenging due to data imbalance and high-dimensional features. In this study, we develop…
Datasets with sheer volume have been generated from fields including computer vision, medical imageology, and astronomy whose large-scale and high-dimensional properties hamper the implementation of classical statistical models. To tackle…
Among the most popular variable selection procedures in high-dimensional regression, Lasso provides a solution path to rank the variables and determines a cut-off position on the path to select variables and estimate coefficients. In this…
The performance of the Lasso is well understood under the assumptions of the standard linear model with homoscedastic noise. However, in several applications, the standard model does not describe the important features of the data. This…
In sparse linear regression, the SLOPE estimator generalizes LASSO by penalizing different coordinates of the estimate according to their magnitudes. In this paper, we present a precise performance characterization of SLOPE in the…
We propose a self-tuning $\sqrt{\mathrm {Lasso}}$ method that simultaneously resolves three important practical problems in high-dimensional regression analysis, namely it handles the unknown scale, heteroscedasticity and (drastic)…
This paper proposes a bootstrap-assisted procedure to conduct simultaneous inference for high dimensional sparse linear models based on the recent de-sparsifying Lasso estimator (van de Geer et al. 2014). Our procedure allows the dimension…
We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality $d$ and small sample size $n$. More specifically, we consider a function…
We propose the variable selection procedure incorporating prior constraint information into lasso. The proposed procedure combines the sample and prior information, and selects significant variables for responses in a narrower region where…
We propose the approximate Laplace approximation (ALA) to evaluate integrated likelihoods, a bottleneck in Bayesian model selection. The Laplace approximation (LA) is a popular tool that speeds up such computation and equips strong model…