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We study a high-dimensional regression model. Aim is to construct a confidence set for a given group of regression coefficients, treating all other regression coefficients as nuisance parameters. We apply a one-step procedure with the…

In this paper, we address the problem of conducting statistical inference in settings involving large-scale data that may be high-dimensional and contaminated by outliers. The high volume and dimensionality of the data require distributed…

The least absolute shrinkage and selection operator (LASSO) for linear regression exploits the geometric interplay of the $\ell_2$-data error objective and the $\ell_1$-norm constraint to arbitrarily select sparse models. Guiding this…

Panel data allows for the modeling of unobserved heterogeneity, significantly raising the number of nuisance parameters and making high dimensionality a practical issue. Meanwhile, temporal and cross-sectional dependence in panel data…

This paper studies the subspace segmentation problem which aims to segment data drawn from a union of multiple linear subspaces. Recent works by using sparse representation, low rank representation and their extensions attract much…

Applied statisticians use sequential regression procedures to produce a ranking of explanatory variables and, in settings of low correlations between variables and strong true effect sizes, expect that variables at the very top of this…

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…

This paper studies the subspace segmentation problem. Given a set of data points drawn from a union of subspaces, the goal is to partition them into their underlying subspaces they were drawn from. The spectral clustering method is used as…

Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control…

We present two sets of theoretical results on the grouped lasso with overlap of Jacob, Obozinski and Vert (2009) in the linear regression setting. This method allows for joint selection of predictors in sparse regression, allowing for…

For data with high-dimensional covariates but small to moderate sample sizes, the analysis of single datasets often generates unsatisfactory results. The integrative analysis of multiple independent datasets provides an effective way of…

In high dimensional regression, feature clustering by their effects on outcomes is often as important as feature selection. For that purpose, clustered Lasso and octagonal shrinkage and clustering algorithm for regression (OSCAR) are used…

In the context of multiple regression model, suppose that the vector parameter of interest \beta is subjected to lie in the subspace hypothesis H\beta = h, where this restriction is based on either additional information or prior knowledge.…

Recommendation systems (RS) aim to provide personalized content, but they face a challenge in unbiased learning due to selection bias, where users only interact with items they prefer. This bias leads to a distorted representation of user…

The purpose of model selection algorithms such as All Subsets, Forward Selection and Backward Elimination is to choose a linear model on the basis of the same set of data to which the model will be applied. Typically we have available a…

In the sparse linear regression setting, we consider testing the significance of the predictor variable that enters the current lasso model, in the sequence of models visited along the lasso solution path. We propose a simple test statistic…

Sparse linear regression (SLR) is a well-studied problem in statistics where one is given a design matrix $X\in\mathbb{R}^{m\times n}$ and a response vector $y=X\theta^*+w$ for a $k$-sparse vector $\theta^*$ (that is, $\|\theta^*\|_0\leq…

For various applications, the relations between the dependent and independent variables are highly nonlinear. Consequently, for large scale complex problems, neural networks and regression trees are commonly preferred over linear models…

This paper introduces a new regularized version of the robust $\tau$-regression estimator for analyzing high-dimensional datasets subject to gross contamination in the response variables and covariates. The resulting estimator, termed…

We consider regression problems where the number of predictors greatly exceeds the number of observations. We propose a method for variable selection that first estimates the regression function, yielding a "pre-conditioned" response…