Non-asymptotic Oracle Inequalities for the Lasso and Group Lasso in high dimensional logistic model
نویسنده
چکیده
We consider the problem of estimating a function f0 in logistic regression model. We propose to estimate this function f0 by a sparse approximation build as a linear combination of elements of a given dictionary of p functions. This sparse approximation is selected by the Lasso or Group Lasso procedure. In this context, we state non asymptotic oracle inequalities for Lasso and Group Lasso under restricted eigenvalues assumption as introduced in [1]. Those theoretical results are illustrated through a simulation study. keywords: Logistic model, Lasso, Group Lasso, High-dimensional.
منابع مشابه
Non-Asymptotic Oracle Inequalities for the High-Dimensional Cox Regression via Lasso.
We consider finite sample properties of the regularized high-dimensional Cox regression via lasso. Existing literature focuses on linear models or generalized linear models with Lipschitz loss functions, where the empirical risk functions are the summations of independent and identically distributed (iid) losses. The summands in the negative log partial likelihood function for censored survival...
متن کاملOracle Inequalities and Selection Consistency for Weighted Lasso in High-dimensional Additive Hazards Model
The additive hazards model has many applications in high-throughput genomic data analysis and clinical studies. In this article, we study the weighted Lasso estimator for the additive hazards model in sparse, high-dimensional settings where the number of time-dependent covariates is much larger than the sample size. Based on compatibility, cone invertibility factors, and restricted eigenvalues ...
متن کاملThe Iterated Lasso for High-Dimensional Logistic Regression
We consider an iterated Lasso approach for variable selection and estimation in sparse, high-dimensional logistic regression models. In this approach, we use the Lasso (Tibshirani 1996) to obtain an initial estimator and reduce the dimension of the model. We then use the Lasso as the initial estimator in the adaptive Lasso (Zou 2006) to obtain the final selection and estimation results. We prov...
متن کاملAsymptotic Equivalence of Regularization Methods in Thresholded Parameter Space
High-dimensional data analysis has motivated a spectrum of regularization methods for variable selection and sparse modeling, with two popular methods being convex and concave ones. A long debate has taken place on whether one class dominates the other, an important question both in theory and to practitioners. In this article, we characterize the asymptotic equivalence of regularization method...
متن کاملThe lasso for high dimensional regression with a possible change point
We consider a high dimensional regression model with a possible change point due to a covariate threshold and develop the lasso estimator of regression coefficients as well as the threshold parameter. Our lasso estimator not only selects covariates but also selects a model between linear and threshold regression models. Under a sparsity assumption, we derive non-asymptotic oracle inequalities f...
متن کامل