Related papers: The Loss Rank Criterion for Variable Selection in …
This paper studies model selection consistency for high dimensional sparse regression when data exhibits both cross-sectional and serial dependency. Most commonly-used model selection methods fail to consistently recover the true model when…
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…
For many scientific questions, understanding the underlying mechanism is the goal. To help investigators better understand the underlying mechanism, variable selection is a crucial step that permits the identification of the most associated…
Regularized models are often sensitive to the scales of the features in the data and it has therefore become standard practice to normalize (center and scale) the features before fitting the model. But there are many different ways to…
We propose a new variable selection procedure for a functional linear model with multiple scalar responses and multiple functional predictors. This method is based on basis expansions of the involved functional predictors and coefficients…
In system identification, estimating parameters of a model using limited observations results in poor identifiability. To cope with this issue, we propose a new method to simultaneously select and estimate sensitive parameters as key model…
Regularization by the sum of singular values, also referred to as the trace norm, is a popular technique for estimating low rank rectangular matrices. In this paper, we extend some of the consistency results of the Lasso to provide…
Recurrent stochastic configuration networks (RSCNs) have shown great potential in modelling nonlinear dynamic systems with uncertainties. This paper presents an RSCN with hybrid regularization to enhance both the learning capacity and…
In generalized linear regression problems with an abundant number of features, lasso-type regularization which imposes an $\ell^1$-constraint on the regression coefficients has become a widely established technique. Deficiencies of the…
Lasso is a popular and efficient approach to simultaneous estimation and variable selection in high-dimensional regression models. In this paper, a robust LAD-lasso method for multiple outcomes is presented that addresses the challenges of…
We study a seemingly unexpected and relatively less understood overfitting aspect of a fundamental tool in sparse linear modeling - best subset selection, which minimizes the residual sum of squares subject to a constraint on the number of…
Regularized linear models, such as Lasso, have attracted great attention in statistical learning and data science. However, there is sporadic work on constructing efficient data collection for regularized linear models. In this work, we…
In high-dimensional data settings where $p\gg n$, many penalized regularization approaches were studied for simultaneous variable selection and estimation. However, with the existence of covariates with weak effect, many existing variable…
Similar to variable selection in the linear regression model, selecting significant components in the popular additive regression model is of great interest. However, such components are unknown smooth functions of independent variables,…
Model selection consistency in the high-dimensional regression setting can be achieved only if strong assumptions are fulfilled. We therefore suggest to pursue a different goal, which we call a minimal class of models. The minimal class of…
We propose a method for variable selection in multiple regression with random predictors. This method is based on a criterion that permits to reduce the variable selection problem to a problem of estimating suitable permutation and…
In a polynomial regression model, the divisibility conditions implicit in polynomial hierarchy give way to a natural construction of constraints for the model parameters. We use this principle to derive versions of strong and weak hierarchy…
The Least Absolute Shrinkage and Selection Operator (LASSO) has gained attention in a wide class of continuous parametric estimation problems with promising results. It has been a subject of research for more than a decade. Due to the…
The application of the lasso is espoused in high-dimensional settings where only a small number of the regression coefficients are believed to be nonzero. Moreover, statistical properties of high-dimensional lasso estimators are often…
Variable screening is a fast dimension reduction technique for assisting high dimensional feature selection. As a preselection method, it selects a moderate size subset of candidate variables for further refining via feature selection to…