Related papers: Sparsity meets correlation in Gaussian sequence mo…

We introduce a very general method for sparse and large-scale variable selection. The large-scale regression settings is such that both the number of parameters and the number of samples are extremely large. The proposed method is based on…

We study a new class of codes for Gaussian multi-terminal source and channel coding. These codes are designed using the statistical framework of high-dimensional linear regression and are called Sparse Superposition or Sparse Regression…

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…

We consider the observations of an unknown $s$-sparse vector ${\boldsymbol \theta}$ corrupted by Gaussian noise with zero mean and unknown covariance matrix ${\boldsymbol \Sigma}$. We propose minimax optimal methods of estimating the…

Given $m$ $d$-dimensional responsors and $n$ $d$-dimensional predictors, sparse regression finds at most $k$ predictors for each responsor for linear approximation, $1\leq k \leq d-1$. The key problem in sparse regression is subset…

This paper investigates the detection and estimation of a single change in high-dimensional linear models. We derive minimax lower bounds for the detection boundary and the estimation rate, which uncover a phase transition governed by the…

We consider estimation of a sparse parameter vector that determines the covariance matrix of a Gaussian random vector via a sparse expansion into known "basis matrices". Using the theory of reproducing kernel Hilbert spaces, we derive lower…

Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence in expectation to…

Sparsity-constrained optimization has wide applicability in machine learning, statistics, and signal processing problems such as feature selection and compressive Sensing. A vast body of work has studied the sparsity-constrained…

We consider the problem of recovering sparse vectors from underdetermined linear measurements via $\ell_p$-constrained basis pursuit. Previous analyses of this problem based on generalized restricted isometry properties have suggested that…

We examine the linear regression problem in a challenging high-dimensional setting with correlated predictors where the vector of coefficients can vary from sparse to dense. In this setting, we propose a combination of probabilistic…

We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections. A few examples where this problem is relevant are compressed sensing, sparse superposition codes, and code division multiple access.…

This paper considers estimation of sparse covariance matrices and establishes the optimal rate of convergence under a range of matrix operator norm and Bregman divergence losses. A major focus is on the derivation of a rate sharp minimax…

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…

We consider the problem of mixed sparse linear regression with two components, where two real $k$-sparse signals $\beta_1, \beta_2$ are to be recovered from $n$ unlabelled noisy linear measurements. The sparsity is allowed to be sublinear…

We consider rank-one symmetric tensor estimation when the tensor is corrupted by Gaussian noise and the spike forming the tensor is a structured signal coming from a generalized linear model. The latter is a mathematically tractable model…

Gaussianization is a simple generative model that can be trained without backpropagation. It has shown compelling performance on low dimensional data. As the dimension increases, however, it has been observed that the convergence speed…

In this paper, we study the problem of sparse mixed linear regression on an unlabeled dataset that is generated from linear measurements from two different regression parameter vectors. Since the data is unlabeled, our task is not only to…

We study least squares linear regression over $N$ uncorrelated Gaussian features that are selected in order of decreasing variance. When the number of selected features $p$ is at most the sample size $n$, the estimator under consideration…

Consider the problem on sequential change-point detection on multiple data streams. We provide the asymptotic lower bounds of the detection delays at all levels of change-point sparsity and we derive a smaller asymptotic lower bound of the…