Related papers: Look-Ahead Screening Rules for the Lasso

Selective Inference (SI) has been actively studied in the past few years for conducting inference on the features of linear models that are adaptively selected by feature selection methods such as Lasso. The basic idea of SI is to make…

Two popular variable screening methods under the ultra-high dimensional setting with the desirable sure screening property are the sure independence screening (SIS) and the forward regression (FR). Both are classical variable screening…

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…

We extend the feature selection methodology to dependent data and propose a novel time series predictor selection scheme that accommodates statistical dependence in a more typical i.i.d sub-sampling based framework. Furthermore, the…

When the design matrix has orthonormal columns, "soft thresholding" the ordinary least squares (OLS) solution produces the Lasso solution [Tibshirani, 1996]. If one uses the Puffer preconditioned Lasso [Jia and Rohe, 2012], then this result…

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…

Feature or variable selection is a problem inherent to large data sets. While many methods have been proposed to deal with this problem, some can scale poorly with the number of predictors in a data set. Screening methods scale linearly…

In this paper, we revisit the large-scale constrained linear regression problem and propose faster methods based on some recent developments in sketching and optimization. Our algorithms combine (accelerated) mini-batch SGD with a new…

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…

The construction of coherent prediction models holds great importance in medical research as such models enable health researchers to gain deeper insights into disease epidemiology and clinicians to identify patients at higher risk of…

A new method is proposed for variable screening, variable selection and prediction in linear regression problems where the number of predictors can be much larger than the number of observations. The method involves minimizing a penalized…

In high-dimensions, many variable selection methods, such as the lasso, are often limited by excessive variability and rank deficiency of the sample covariance matrix. Covariance sparsity is a natural phenomenon in high-dimensional…

Forward-backward selection is one of the most basic and commonly-used feature selection algorithms available. It is also general and conceptually applicable to many different types of data. In this paper, we propose a heuristic that…

Regularized regression approaches such as the Lasso have been widely adopted for constructing sparse linear models in high-dimensional datasets. A complexity in fitting these models is the tuning of the parameters which control the level of…

Many recent developments in the high-dimensional statistical time series literature have centered around time-dependent applications that can be adapted to regularized least squares. Of particular interest is the lasso, which both serves to…

The estimation of a precision matrix is a crucial problem in various research fields, particularly when working with high dimensional data. In such settings, the most common approach is to use the penalized maximum likelihood. The…

Penalized regression is an attractive framework for variable selection problems. Often, variables possess a grouping structure, and the relevant selection problem is that of selecting groups, not individual variables. The group lasso has…

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…

We address the challenge of correlated predictors in high-dimensional GLMs, where regression coefficients range from sparse to dense, by proposing a data-driven random projection method. This is particularly relevant for applications where…

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…