Related papers: Sparse recovery with unknown variance: a LASSO-typ…

The problem of recovering the sparsity pattern of a fixed but unknown vector $\beta^* \in \real^p based on a set of $n$ noisy observations arises in a variety of settings, including subset selection in regression, graphical model selection,…

Sparse linear regression -- finding an unknown vector from linear measurements -- is now known to be possible with fewer samples than variables, via methods like the LASSO. We consider the multiple sparse linear regression problem, where…

In this paper we present a linear programming solution for sign pattern recovery of a sparse signal from noisy random projections of the signal. We consider two types of noise models, input noise, where noise enters before the random…

We consider the problem of recovering a $k$-sparse signal ${\mbox{$\beta$}}_0\in\mathbb{R}^p$ from noisy observations $\bf y={\bf X}\mbox{$\beta$}_0+{\bf w}\in\mathbb{R}^n$. One of the most popular approaches is the $l_1$-regularized least…

We study sparse linear regression over a network of agents, modeled as an undirected graph (with no centralized node). The estimation problem is formulated as the minimization of the sum of the local LASSO loss functions plus a quadratic…

Recovery of the sparsity pattern (or support) of an unknown sparse vector from a limited number of noisy linear measurements is an important problem in compressed sensing. In the high-dimensional setting, it is known that recovery with a…

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 $n \times m$…

This paper is concerned with inference about low-dimensional components of a high-dimensional parameter vector $\beta^0$ which is identified through instrumental variables. We allow for eigenvalues of the expected outer product of included…

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…

We consider the high-dimensional linear regression model $Y = X \beta^0 + \epsilon$ with Gaussian noise $\epsilon$ and Gaussian random design $X$. We assume that $\Sigma:= E X^T X / n$ is non-singular and write its inverse as $\Theta :=…

Modern statistical learning algorithms are capable of amazing flexibility, but struggle with interpretability. One possible solution is sparsity: making inference such that many of the parameters are estimated as being identically 0, which…

We consider the problem of recovering a vector $\beta_o \in \mathbb{R}^p$ from $n$ random and noisy linear observations $y= X\beta_o + w$, where $X$ is the measurement matrix and $w$ is noise. The LASSO estimate is given by the solution to…

We propose a new algorithm for recovery of sparse signals from their compressively sensed samples. The proposed algorithm benefits from the strategy of gradual movement to estimate the positions of non-zero samples of sparse signal. We…

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 $\beta \in {\mathbb R}^p$…

Confidence intervals based on penalized maximum likelihood estimators such as the LASSO, adaptive LASSO, and hard-thresholding are analyzed. In the known-variance case, the finite-sample coverage properties of such intervals are determined…

We present a detailed analysis of the unconstrained $\ell_1$-weighted LASSO method for recovery of sparse data from its observation by randomly generated matrices, satisfying the Restricted Isometry Property (RIP) with constant $\delta<1$,…

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.…

Many problems in classification involve huge numbers of irrelevant features. Model selection reveals the crucial features, reduces the dimensionality of feature space, and improves model interpretation. In the support vector machine…

We consider machine learning techniques to develop low-latency approximate solutions to a class of inverse problems. More precisely, we use a probabilistic approach for the problem of recovering sparse stochastic signals that are members of…

For statistical analysis of network data, the $\beta$-model has emerged as a useful tool, thanks to its flexibility in incorporating nodewise heterogeneity and theoretical tractability. To generalize the $\beta$-model, this paper proposes…