Related papers: Variable Selection with Exponential Weights and $l…
We establish theoretical guarantees for the expected prediction error of the exponential weighting aggregate in the case of multivariate regression that is when the label vector is multidimensional. We consider the regression model with…
In the causal adjustment setting, variable selection techniques based on either the outcome or treatment allocation model can result in the omission of confounders or the inclusion of spurious variables in the propensity score. We propose a…
We consider the problem of automatic variable selection in a linear model with asymmetric or heavy-tailed errors when the number of explanatory variables diverges with the sample size. For this high-dimensional model, the penalized least…
We give oracle inequalities on procedures which combines quantization and variable selection via a weighted Lasso $k$-means type algorithm. The results are derived for a general family of weights, which can be tuned to size the influence of…
We consider the sparse regression model where the number of parameters $p$ is larger than the sample size $n$. The difficulty when considering high-dimensional problems is to propose estimators achieving a good compromise between…
We develop a set of variable selection methods for the Cox model under interval censoring, in the ultra-high dimensional setting where the dimensionality can grow exponentially with the sample size. The methods select covariates via a…
When we are interested in high-dimensional system and focus on classification performance, the $\ell_{1}$-penalized logistic regression is becoming important and popular. However, the Lasso estimates could be problematic when penalties of…
In the causal adjustment setting, variable selection techniques based on one of either the outcome or treatment allocation model can result in the omission of confounders, which leads to bias, or the inclusion of spurious variables, which…
We consider the problem of recovering an unknown vector from noisy data with the help of projection estimates. The goal is to find a convex combination of these estimates with the minimal risk. We study an aggregation method based on the…
A new empirical Bayes approach to variable selection in the context of generalized linear models is developed. The proposed algorithm scales to situations in which the number of putative explanatory variables is very large, possibly much…
Consider a regression model with fixed design and Gaussian noise where the regression function can potentially be well approximated by a function that admits a sparse representation in a given dictionary. This paper resorts to exponential…
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…
We consider a Bayesian approach to model selection in Gaussian linear regression, where the number of predictors might be much larger than the number of observations. From a frequentist view, the proposed procedure results in the penalized…
This paper focuses on variable selection for a partially linear single-index varying-coefficient model. A regularized variable selection procedure by combining basis function approximations with SCAD penalty is proposed. It can…
The performance of Orthogonal Matching Pursuit (OMP) for variable selection is analyzed for random designs. When contrasted with the deterministic case, since the performance is here measured after averaging over the distribution of the…
We study various constraints and conditions on the true coefficient vector and on the design matrix to establish non-asymptotic oracle inequalities for the prediction error, estimation accuracy and variable selection for the Lasso estimator…
The standard quantile regression model assumes a linear relationship at the quantile of interest and that all variables are observed. We relax these assumptions by considering a partial linear model while allowing for missing linear…
We discuss the fundamental issue of identification in linear instrumental variable (IV) models with unknown IV validity. With the assumption of the "sparsest rule", which is equivalent to the plurality rule but becomes operational in…
We propose a method for variable selection and basis learning for high-dimensional classification with ordinal responses. The proposed method extends sparse multiclass linear discriminant analysis, with the aim of identifying not only the…
In this paper, we consider Bayesian variable selection problem of linear regression model with global-local shrinkage priors on the regression coefficients. We propose a variable selection procedure that select a variable if the ratio of…