Related papers: On cross-validated Lasso in high dimensions

A new estimator, named S-LASSO, is proposed for the coefficient function of the Function-on-Function linear regression model. The S-LASSO estimator is shown to be able to increase the interpretability of the model, by better locating…

Stochastic approximation is a powerful class of algorithms with celebrated success. However, a large body of previous analysis focuses on stochastic approximations driven by contractive operators, which is not applicable in some important…

Cross-validation (CV) is often used to select the regularization parameter in high dimensional problems. However, when applied to the sparse modeling method Lasso, CV leads to models that are unstable in high-dimensions, and consequently…

The problems of Lasso regression and optimal design of experiments share a critical property: their optimal solutions are typically \emph{sparse}, i.e., only a small fraction of the optimal variables are non-zero. Therefore, the…

The graphical lasso is a widely used algorithm for fitting undirected Gaussian graphical models. However, for inference on functionals of edge values in the learned graph, standard tools lack formal statistical guarantees, such as control…

We study the asymptotic properties of Lasso+mLS and Lasso+Ridge under the sparse high-dimensional linear regression model: Lasso selecting predictors and then modified Least Squares (mLS) or Ridge estimating their coefficients. First, we…

This work performs a non-asymptotic analysis of the generalized Lasso under the assumption of sub-exponential data. Our main results continue recent research on the benchmark case of (sub-)Gaussian sample distributions and thereby explore…

We consider high-dimensional inference for potentially misspecified Cox proportional hazard models based on low dimensional results by Lin and Wei [1989]. A de-sparsified Lasso estimator is proposed based on the log partial likelihood…

We consider the problem of sparse signal recovery from noisy measurements. Many of frequently used recovery methods rely on some sort of tuning depending on either noise or signal parameters. If no estimates for either of them are…

This paper focuses on random projection operators when the subspace of projection is estimated. We derive non-asymptotic upper bounds on the error between the projection onto the estimated subspace and the projection onto the underlying…

In regression problems where covariates can be naturally grouped, the group Lasso is an attractive method for variable selection since it respects the grouping structure in the data. We study the selection and estimation properties of the…

Despite its prevalence in statistical datasets, heteroscedasticity (non-constant sample variances) has been largely ignored in the high-dimensional statistics literature. Recently, studies have shown that the Lasso can accommodate…

We investigate a robust penalized logistic regression algorithm based on a minimum distance criterion. Influential outliers are often associated with the explosion of parameter vector estimates, but in the context of standard logistic…

This paper investigates the effect of the design matrix on the ability (or inability) to estimate a sparse parameter in linear regression. More specifically, we characterize the optimal rate of estimation when the smallest singular value of…

In a recent article (Proc. Natl. Acad. Sci., 110(36), 14557-14562), El Karoui et al. study the distribution of robust regression estimators in the regime in which the number of parameters p is of the same order as the number of samples n.…

The lasso is a popular tool for sparse linear regression, especially for problems in which the number of variables p exceeds the number of observations n. But when p>n, the lasso criterion is not strictly convex, and hence it may not have a…

The Lasso is a popular model selection and estimation procedure for linear models that enjoys nice theoretical properties. In this paper, we study the Lasso estimator for fitting autoregressive time series models. We adopt a double…

We study the Cox models with semiparametric relative risk, which can be partially linear with one nonparametric component, or multiple additive or nonadditive nonparametric components. A penalized partial likelihood procedure is proposed to…

In this note, we propose to use sparse methods (e.g. LASSO, Post-LASSO, sqrt-LASSO, and Post-sqrt-LASSO) to form first-stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments in…

An asymptotically optimal blind calibration scheme of uniform linear arrays for narrowband Gaussian signals is proposed. Rather than taking the direct Maximum Likelihood (ML) approach for joint estimation of all the unknown model…