Related papers: Transductive versions of the LASSO and the Dantzig…
To estimate a sparse linear model from data with Gaussian noise, consilience from lasso and compressed sensing literatures is that thresholding estimators like lasso and the Dantzig selector have the ability in some situations to identify…
A multiple interval-valued linear regression model considering all the cross-relationships between the mids and spreads of the intervals has been introduced recently. A least-squares estimation of the regression parameters has been carried…
The Dantzig selector for a special parametric model of diffusion processes is studied in this paper. In our model, the diffusion coefficient is given as the exponential of the linear combination of other processes which are regarded as…
In many applications one may acquire a composition of several signals that may be corrupted by noise, and it is a challenging problem to reliably separate the components from one another without sacrificing significant details. Adding to…
Given data $y$ and $k$ covariates $x$ one problem in linear regression is to decide which in any of the covariates to include when regressing $y$ on the $x$. If $k$ is small it is possible to evaluate each subset of the $x$. If however $k$…
Discussion of ``The Dantzig selector: Statistical estimation when $p$ is much larger than $n$'' [math/0506081]
We consider the sparse regression model where the number of parameters $p$ is larger than the sample size $n$. The difficulty when considering high-dimensional problems is to propose estimators achieving a good compromise between…
We study the limitations of the well known LASSO regression as a variable selector when there exists dependence structures among covariates. We analyze both the classic situation with $n\geq p$ and the high dimensional framework with $p>n$.…
Discussion of ``The Dantzig selector: Statistical estimation when $p$ is much larger than $n$'' [math/0506081]
Discussion of ``The Dantzig selector: Statistical estimation when $p$ is much larger than $n$'' [math/0506081]
Discussion of ``The Dantzig selector: Statistical estimation when $p$ is much larger than $n$'' [math/0506081]
The Lasso is a method for high-dimensional regression, which is now commonly used when the number of covariates $p$ is of the same order or larger than the number of observations $n$. Classical asymptotic normality theory does not apply to…
Modern statistical analysis often encounters high-dimensional problems but with a limited sample size. It poses great challenges to traditional statistical estimation methods. In this work, we adopt auxiliary learning to solve the…
Sparse linear inverse problems appear in a variety of settings, but often the noise contaminating observations cannot accurately be described as bounded by or arising from a Gaussian distribution. Poisson observations in particular are a…
The Dantzig selector (Candes and Tao, 2007) is a popular l1-regularization method for variable selection and estimation in linear regression. We present a very weak geometric condition on the observed predictors which is related to…
Discussion of "The Dantzig selector: Statistical estimation when $p$ is much larger than $n$" [math/0506081]
The least absolute shrinkage and selection operator (LASSO) is a popular technique for simultaneous estimation and model selection. There have been a lot of studies on the large sample asymptotic distributional properties of the LASSO…
High-dimensional statistical settings ($p \gg n$) pose fundamental challenges for classical inference, largely due to bias introduced by regularized estimators such as the LASSO. To address this, Javanmard and Montanari (2014) propose a…
To successfully work on variable selection, sparse model structure has become a basic assumption for all existing methods. However, this assumption is questionable as it is hard to hold in most of cases and none of existing methods may…
We propose a novel high-dimensional linear regression estimator: the Discrete Dantzig Selector, which minimizes the number of nonzero regression coefficients subject to a budget on the maximal absolute correlation between the features and…