相关论文: The sparsity and bias of the Lasso selection in hi…

This paper is concerned with high-dimensional panel data models where the number of regressors can be much larger than the sample size. Under the assumption that the true parameter vector is sparse we propose a panel-Lasso estimator and…

We consider the linear regression problem. We propose the S-Lasso procedure to estimate the unknown regression parameters. This estimator enjoys sparsity of the representation while taking into account correlation between successive…

Recent work has focused on the problem of conducting linear regression when the number of covariates is very large, potentially greater than the sample size. To facilitate this, one useful tool is to assume that the model can be well…

Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…

Given $n$ noisy samples with $p$ dimensions, where $n \ll p$, we show that the multi-step thresholding procedure based on the Lasso -- we call it the {\it Thresholded Lasso}, can accurately estimate a sparse vector $\beta \in \R^p$ in a…

In the high-dimensional regression model a response variable is linearly related to $p$ covariates, but the sample size $n$ is smaller than $p$. We assume that only a small subset of covariates is `active' (i.e., the corresponding…

We study the theoretical properties of the fused lasso procedure originally proposed by \cite{tibshirani2005sparsity} in the context of a linear regression model in which the regression coefficient are totally ordered and assumed to be…

The lasso has become an important practical tool for high dimensional regression as well as the object of intense theoretical investigation. But despite the availability of efficient algorithms, the lasso remains computationally demanding…

We present upper and lower bounds for the prediction error of the Lasso. For the case of random Gaussian design, we show that under mild conditions the prediction error of the Lasso is up to smaller order terms dominated by the prediction…

The problem of consistently estimating the sparsity pattern of a vector $\betastar \in \real^\mdim$ based on observations contaminated by noise arises in various contexts, including subset selection in regression, structure estimation in…

Lasso and other regularization procedures are attractive methods for variable selection, subject to a proper choice of shrinkage parameter. Given a set of potential subsets produced by a regularization algorithm, a consistent model…

The Lasso is a prominent algorithm for variable selection. However, its instability in the presence of correlated variables in the high-dimensional setting is well-documented. Although previous research has attempted to address this issue…

In this paper, we review state-of-the-art methods for feature selection in statistics with an application-oriented eye. Indeed, sparsity is a valuable property and the profusion of research on the topic might have provided little guidance…

This paper proposes a multi-stage projection-based Lasso procedure for the semiparametric sample selection model in high-dimensional settings under a weak nonparametric restriction on the selection correction. In particular, the number of…

Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…

In regression settings where explanatory variables have very low correlations and there are relatively few effects, each of large magnitude, we expect the Lasso to find the important variables with few errors, if any. This paper shows that…

High-dimensional settings, where the data dimension ($d$) far exceeds the number of observations ($n$), are common in many statistical and machine learning applications. Methods based on $\ell_1$-relaxation, such as Lasso, are very popular…

We propose a new approach to safe variable preselection in high-dimensional penalized regression, such as the lasso. Preselection - to start with a manageable set of covariates - has often been implemented without clear appreciation of its…

We study sparse group Lasso for high-dimensional double sparse linear regression, where the parameter of interest is simultaneously element-wise and group-wise sparse. This problem is an important instance of the simultaneously structured…

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…