Name
Title | ||
|---|---|---|
Estimation and Selection via Absolute Penalized Convex Minimization And Its Multistage Adaptive Applications. |
Abstract | ||
|---|---|---|
The ℓ1-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 high-dimensional statistical problems. In this article, we consider a class of weighted ℓ1-penalized estimators for convex loss functions of a general form, including the generalized linear models. We study the estimation, prediction, selection and sparsity properties of the weighted ℓ1-penalized estimator in sparse, high-dimensional settings where the number of predictors p can be much larger than the sample size n. Adaptive Lasso is considered as a special case. A multistage method is developed to approximate concave regularized estimation by applying an adaptive Lasso recursively. We provide prediction and estimation oracle inequalities for single- and multi-stage estimators, a general selection consistency theorem, and an upper bound for the dimension of the Lasso estimator. Important models including the linear regression, logistic regression and log-linear models are used throughout to illustrate the applications of the general results. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.5555/2188385.2343702 | Journal of Machine Learning Research |
Keywords | Field | DocType |
generalized linear models,approximate concave regularized estimation,linear regression,estimation oracle inequality,adaptive lasso,selection consistency,general result,adaptive lasso recursively,lasso estimator,general form,l1-penalized estimator,multistage adaptive application,oracle inequality,penalized estimation,sparsity,variable selection,absolute penalized convex minimization,general selection consistency theorem,bioinformatics,biomedical research | Feature selection,Upper and lower bounds,Elastic net regularization,Lasso (statistics),Generalized linear model,Artificial intelligence,Convex optimization,Machine learning,Mathematics,Estimator,Linear regression | Journal |
Volume | Issue | ISSN |
13 | 1 | 1532-4435 |
Citations | PageRank | References |
4 | 0.65 | 28 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jian Huang | 1 | 2608 | 200.50 |
| Cun-Hui Zhang | 2 | 174 | 18.38 |