Related papers: Lasso-Ridge Refitting: A Two-Stage Estimator for H…
Convex estimators such as the Lasso, the matrix Lasso and the group Lasso have been studied extensively in the last two decades, demonstrating great success in both theory and practice. Two quantities are introduced, the noise barrier and…
The nonnegative garrote (NNG) is among the first approaches that combine variable selection and shrinkage of regression estimates. When more than the derivation of a predictor is of interest, NNG has some conceptual advantages over the…
Penalized (or regularized) regression, as represented by Lasso and its variants, has become a standard technique for analyzing high-dimensional data when the number of variables substantially exceeds the sample size. The performance of…
The Lasso has become a benchmark data analysis procedure, and numerous variants have been proposed in the literature. Although the Lasso formulations are stated so that overall prediction error is optimized, no full control over the…
For high-dimensional omics data, sparsity-inducing regularization methods such as the Lasso are widely used and often yield strong predictive performance, even in settings when the assumption of sparsity is likely violated. We demonstrate…
In this paper, a new ridge-type shrinkage estimator for the precision matrix has been proposed. The asymptotic optimal shrinkage coefficients and the theoretical loss were derived. Data-driven estimators for the shrinkage coefficients were…
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 fused lasso is an important method for signal processing when the hidden signals are sparse and blocky. It is often used in combination with the squared loss function. However, the squared loss is not suitable for heavy tail error…
We study the performance of sparse regression methods and propose new techniques to distill the governing equations of dynamical systems from data. We first look at the generic methodology of learning interpretable equation forms from data,…
We present a framework for performing efficient regression in general metric spaces. Roughly speaking, our regressor predicts the value at a new point by computing a Lipschitz extension --- the smoothest function consistent with the…
We introduce a discriminative regression approach to supervised classification in this paper. It estimates a representation model while accounting for discriminativeness between classes, thereby enabling accurate derivation of categorical…
Linear regression with normally distributed errors - including particular cases such as ANOVA, Student's t-test or location-scale inference - is a widely used statistical procedure. In this case the ordinary least squares estimator…
The lasso is the most famous sparse regression and feature selection method. One reason for its popularity is the speed at which the underlying optimization problem can be solved. Sorted L-One Penalized Estimation (SLOPE) is a…
A great deal of interest has recently focused on conducting inference on the parameters in a high-dimensional linear model. In this paper, we consider a simple and very na\"{i}ve two-step procedure for this task, in which we (i) fit a lasso…
In additive models with many nonparametric components, a number of regularized estimators have been proposed and proven to attain various error bounds under different combinations of sparsity and fixed smoothness conditions. Some of these…
We consider statistical inference for a single coordinate of regression coefficients in high-dimensional linear models. Recently, the debiased estimators are popularly used for constructing confidence intervals and hypothesis testing in…
Regularized regression techniques for linear regression have been created the last few ten years to reduce the flaws of ordinary least squares regression with regard to prediction accuracy. In this paper, new methods for using regularized…
The beta regression model is a useful framework to model response variables that are rates or proportions, that is to say, response variables which are continuous and restricted to the interval (0,1). As with any other regression model,…
We study the nested model averaging method on the solution path for a high-dimensional linear regression problem. In particular, we propose to combine model averaging with regularized estimators (e.g., lasso and SLOPE) on the solution path…
We propose a novel approach to elicit the weight of a potentially non-stationary regressor in the consistent and oracle-efficient estimation of autoregressive models using the adaptive Lasso. The enhanced weight builds on a statistic that…