Related papers: One-step sparse estimates in nonconcave penalized …

Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is…

We consider the problem of sparse estimation in a factor analysis model. A traditional estimation procedure in use is the following two-step approach: the model is estimated by maximum likelihood method and then a rotation technique is…

A class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed by Fan and Li to simultaneously estimate parameters and select important variables. They demonstrated that this class of…

The statistics literature of the past 15 years has established many favorable properties for sparse diminishing-bias regularization: techniques which can roughly be understood as providing estimation under penalty functions spanning the…

Recently, there has been focus on penalized log-likelihood covariance estimation for sparse inverse covariance (precision) matrices. The penalty is responsible for inducing sparsity, and a very common choice is the convex $l_1$ norm.…

The Lasso is biased. Concave penalized least squares estimation (PLSE) takes advantage of signal strength to reduce this bias, leading to sharper error bounds in prediction, coefficient estimation and variable selection. For prediction and…

Two important goals of high-dimensional modeling are prediction and variable selection. In this article, we consider regularization with combined $L_1$ and concave penalties, and study the sampling properties of the global optimum of the…

Discussion of ``One-step sparse estimates in nonconcave penalized likelihood models'' [arXiv:0808.1012]

Discussion of ``One-step sparse estimates in nonconcave penalized likelihood models'' [arXiv:0808.1012]

Partial penalized tests provide flexible approaches to testing linear hypotheses in high dimensional generalized linear models. However, because the estimators used in these tests are local minimizers of potentially non-convex…

We consider the problem of selecting covariates in spatial linear models with Gaussian process errors. Penalized maximum likelihood estimation (PMLE) that enables simultaneous variable selection and parameter estimation is developed and,…

High-dimensional sparse modeling with censored survival data is of great practical importance, as exemplified by modern applications in high-throughput genomic data analysis and credit risk analysis. In this article, we propose a class of…

The Ising model is a useful tool for studying complex interactions within a system. The estimation of such a model, however, is rather challenging, especially in the presence of high-dimensional parameters. In this work, we propose…

Penalized likelihood methods are fundamental to ultra-high dimensional variable selection. How high dimensionality such methods can handle remains largely unknown. In this paper, we show that in the context of generalized linear models,…

We propose a new penalized method for variable selection and estimation that explicitly incorporates the correlation patterns among predictors. This method is based on a combination of the minimax concave penalty and Laplacian quadratic…

In high-dimensional data analysis, penalized likelihood estimators are shown to provide superior results in both variable selection and parameter estimation. A new algorithm, APPLE, is proposed for calculating the Approximate Path for…

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 consider the problem of estimation of a covariance matrix for Gaussian data in a high dimensional setting. Existing approaches include maximum likelihood estimation under a pre-specified sparsity pattern, l_1-penalized loglikelihood…

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…

We propose a new algorithm---Stochastic Proximal Langevin Algorithm (SPLA)---for sampling from a log concave distribution. Our method is a generalization of the Langevin algorithm to potentials expressed as the sum of one stochastic smooth…