Related papers: De-biasing the Lasso: Optimal Sample Size for Gaus…

Statistical inference on the explained variation of an outcome by a set of covariates is of particular interest in practice. When the covariates are of moderate to high-dimension and the effects are not sparse, several approaches have been…

We study the problem of detection of a p-dimensional sparse vector of parameters in the linear regression model with Gaussian noise. We establish the detection boundary, i.e., the necessary and sufficient conditions for the possibility of…

We develop a scalable class of models for latent variable estimation using composite Gaussian processes, with a focus on derivative Gaussian processes. We jointly model multiple data sources as outputs to improve the accuracy of latent…

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…

Consider the Gaussian vector model with mean value {\theta}. We study the twin problems of estimating the number |{\theta}|_0 of non-zero components of {\theta} and testing whether |{\theta}|_0 is smaller than some value. For testing, we…

We derive expressions for the finite-sample distribution of the Lasso estimator in the context of a linear regression model in low as well as in high dimensions by exploiting the structure of the optimization problem defining the estimator.…

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…

We study efficient algorithms for linear regression and covariance estimation in the absence of Gaussian assumptions on the underlying distributions of samples, making assumptions instead about only finitely-many moments. We focus on how…

We investigate the high-dimensional linear regression problem in the presence of noise correlated with Gaussian covariates. This correlation, known as endogeneity in regression models, often arises from unobserved variables and other…

Differential entropy and log determinant of the covariance matrix of a multivariate Gaussian distribution have many applications in coding, communications, signal processing and statistical inference. In this paper we consider in the high…

Suppose that we observe $y \in \mathbb{R}^n$ and $X \in \mathbb{R}^{n \times m}$ in the following errors-in-variables model: \begin{eqnarray*} y & = & X_0 \beta^* +\epsilon \\ X & = & X_0 + W, \end{eqnarray*} where $X_0$ is an $n \times m$…

The lasso has been studied extensively as a tool for estimating the coefficient vector in the high-dimensional linear model; however, considerably less is known about estimating the error variance in this context. In this paper, we propose…

In this paper we develop inference for high dimensional linear models, with serially correlated errors. We examine Lasso under the assumption of strong mixing in the covariates and error process, allowing for fatter tails in their…

We consider drawing statistical inferences based on data subject to non-Gaussian measurement error. Unlike most existing methods developed under the assumption of Gaussian measurement error, the proposed strategy exploits hypercomplex…

We propose a test of many zero parameter restrictions in a high dimensional linear iid regression model with $k$ $>>$ $n$ regressors. The test statistic is formed by estimating key parameters one at a time based on many low dimension…

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 a sparse high dimensional regression model where the goal is to recover a $k$-sparse unknown vector $\beta^*$ from $n$ noisy linear observations of the form $Y=X\beta^*+W \in \mathbb{R}^n$ where $X \in \mathbb{R}^{n \times p}$…

In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a…

Recently, many machine learning and statistical models such as non-linear regressions, the Single Index, Multi-index, Varying Coefficient Index Models and Two-layer Neural Networks can be reduced to or be seen as a special case of a new…

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…