Related papers: Estimation And Selection Via Absolute Penalized Co…
This paper studies macroeconomic forecasting and variable selection using a folded-concave penalized regression with a very large number of predictors. The penalized regression approach leads to sparse estimates of the regression…
We propose an $\ell_1$-penalized estimation procedure for high-dimensional linear mixed-effects models. The models are useful whenever there is a grouping structure among high-dimensional observations, i.e. for clustered data. We prove a…
This paper studies oracle properties of $\ell_1$-penalized least squares in nonparametric regression setting with random design. We show that the penalized least squares estimator satisfies sparsity oracle inequalities, i.e., bounds in…
Sorted $\ell_1$ Penalized Estimator (SLOPE) is a relatively new convex regularization method for fitting high-dimensional regression models. SLOPE allows to reduce the model dimension by shrinking some estimates of the regression…
We present a novel approach to the formulation and the resolution of sparse Linear Discriminant Analysis (LDA). Our proposal, is based on penalized Optimal Scoring. It has an exact equivalence with penalized LDA, contrary to the multi-class…
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…
Sparse regularization such as $\ell_1$ regularization is a quite powerful and widely used strategy for high dimensional learning problems. The effectiveness of sparse regularization has been supported practically and theoretically by…
This paper introduces a new regularized version of the robust $\tau$-regression estimator for analyzing high-dimensional datasets subject to gross contamination in the response variables and covariates. The resulting estimator, termed…
The expectation-maximization (EM) algorithm and its variants are widely used in statistics. In high-dimensional mixture linear regression, the model is assumed to be a finite mixture of linear regression and the number of predictors is much…
We present a new approach to solve the sparse approximation or best subset selection problem, namely find a $k$-sparse vector ${\bf x}\in\mathbb{R}^d$ that minimizes the $\ell_2$ residual $\lVert A{\bf x}-{\bf y} \rVert_2$. We consider a…
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…
This paper presents a novel projection-based adaptive algorithm for sparse signal and system identification. The sequentially observed data are used to generate an equivalent sequence of closed convex sets, namely hyperslabs. Each hyperslab…
A sparse modeling is a major topic in machine learning and statistics. LASSO (Least Absolute Shrinkage and Selection Operator) is a popular sparse modeling method while it has been known to yield unexpected large bias especially at a sparse…
In sparse regression modeling via regularization such as the lasso, it is important to select appropriate values of tuning parameters including regularization parameters. The choice of tuning parameters can be viewed as a model selection…
We consider a general high-dimensional additive hazard model in a non-asymptotic setting, including regression for censored-data. In this context, we consider a Lasso estimator with a fully data-driven $\ell_1$ penalization, which is tuned…
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…
Lasso is a celebrated method for variable selection in linear models, but it faces challenges when the variables are moderately or strongly correlated. This motivates alternative approaches such as using a non-convex penalty, adding a ridge…
Statistical methods with empirical likelihood (EL) are appealing and effective especially in conjunction with estimating equations through which useful data information can be adaptively and flexibly incorporated. It is also known in the…
Censored data are quite common in statistics and have been studied in depth in the last years. In this paper we consider censored high-dimensional data. High-dimensional models are in some way more complex than their low-dimensional…
Predicting clinical variables from whole-brain neuroimages is a high dimensional problem that requires some type of feature selection or extraction. Penalized regression is a popular embedded feature selection method for high dimensional…