Related papers: Selection of variables and decision boundaries for…
Sparse logistic regression is for classification and feature selection simultaneously. Although many studies have been done to solve $\ell_1$-regularized logistic regression, there is no equivalently abundant work on solving sparse logistic…
A new sparse semiparametric model is proposed, which incorporates the influence of two functional random variables in a scalar response in a flexible and interpretable manner. One of the functional covariates is included through a…
We investigate fast methods that allow to quickly eliminate variables (features) in supervised learning problems involving a convex loss function and a $l_1$-norm penalty, leading to a potentially substantial reduction in the number of…
This paper investigates correct variable selection in finite samples via $\ell_1$ and $\ell_1+\ell_2$ type penalization schemes. The asymptotic consistency of variable selection immediately follows from this analysis. We focus on logistic…
Ordinal data are quite common in applied statistics. Although some model selection and regularization techniques for categorical predictors and ordinal response models have been developed over the past few years, less work has been done…
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 consider the functional regression model with multivariate response and functional predictors. Compared to fitting each individual response variable separately, taking advantage of the correlation between the response variables can…
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…
Penalized likelihood approaches are widely used for high-dimensional regression. Although many methods have been proposed and the associated theory is now well-developed, the relative efficacy of different approaches in finite-sample…
The two primary approaches for high-dimensional regression problems are sparse methods (e.g., best subset selection, which uses the L0-norm in the penalty) and ensemble methods (e.g., random forests). Although sparse methods typically yield…
Categorical regressor variables are usually handled by introducing a set of indicator variables, and imposing a linear constraint to ensure identifiability in the presence of an intercept, or equivalently, using one of various coding…
Model selection in penalized regression critically depends on an accurate assessment of model complexity, commonly quantified through the effective degrees of freedom. While the Lasso admits a simple and unbiased characterization, given by…
We consider the estimation of a sparse factor model where the factor loading matrix is assumed sparse. The estimation problem is reformulated as a penalized M-estimation criterion, while the restrictions for identifying the factor loading…
The tuning parameter selection strategy for penalized estimation is crucial to identify a model that is both interpretable and predictive. However, popular strategies (e.g., minimizing average squared prediction error via cross-validation)…
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…
During the last decades, many methods for the analysis of functional data including classification methods have been developed. Nonetheless, there are issues that have not been adressed satisfactorily by currently available methods, as, for…
Regression by composition provides a flexible framework for constructing conditional distributions through sequential group actions. However, when multiple flows act on the same distribution, the model becomes non-identifiable, leading to…
This paper considers the problem of variable selection in regression models in the case of functional variables that may be mixed with other type of variables (scalar, multivariate, directional, etc.). Our proposal begins with a simple null…
We consider nonlinear mixed effects models including high-dimensional covariates to model individual parameters variability. The objective is to identify relevant covariates among a large set under sparsity assumption and to estimate model…
We propose an approach for fitting linear regression models that splits the set of covariates into groups. The optimal split of the variables into groups and the regularized estimation of the regression coefficients are performed by…