Related papers: Efficient Statistics for Sparse Graphical Models f…

The stochastic gradient descent (SGD) algorithm has been widely used in statistical estimation for large-scale data due to its computational and memory efficiency. While most existing works focus on the convergence of the objective function…

We study linear models under heavy-tailed priors from a probabilistic viewpoint. Instead of computing a single sparse most probable (MAP) solution as in standard deterministic approaches, the focus in the Bayesian compressed sensing…

In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…

The results of a series of theoretical studies are reported, examining the convergence rate for different approximate representations of $\alpha$-stable distributions. Although they play a key role in modelling random processes with jumps…

This paper investigates total variation minimization in one spatial dimension for the recovery of gradient-sparse signals from undersampled Gaussian measurements. Recently established bounds for the required sampling rate state that uniform…

In high-dimensional generalized linear models, it is crucial to identify a sparse model that adequately accounts for response variation. Although the best subset section has been widely regarded as the Holy Grail of problems of this type,…

We revisit the problem of robust linear regression under Gaussian covariates with an unknown covariance matrix of condition number $\kappa$. For this fundamental problem, significant gaps remain in our understanding of the trade-offs among…

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 propose a novel statistical inference methodology for multiway count data that is corrupted by false zeros that are indistinguishable from true zero counts. Our approach consists of zero-truncating the Poisson distribution to neglect all…

We consider the problem of exact recovery of a $k$-sparse binary vector from generalized linear measurements (such as logistic regression). We analyze the linear estimation algorithm (Plan, Vershynin, Yudovina, 2017), and also show…

Consider the standard Gaussian linear regression model $Y=X\theta+\epsilon$, where $Y\in R^n$ is a response vector and $ X\in R^{n*p}$ is a design matrix. Numerous work have been devoted to building efficient estimators of $\theta$ when $p$…

In compressive sensing, a small collection of linear projections of a sparse signal contains enough information to permit signal recovery. Distributed compressive sensing (DCS) extends this framework by defining ensemble sparsity models,…

The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience…

Handling big data has largely been a major bottleneck in traditional statistical models. Consequently, when accurate point prediction is the primary target, machine learning models are often preferred over their statistical counterparts for…

In this paper we discuss the variable selection method from \ell0-norm constrained regression, which is equivalent to the problem of finding the best subset of a fixed size. Our study focuses on two aspects, consistency and computation. We…

To model modern large-scale datasets, we need efficient algorithms to infer a set of $P$ unknown model parameters from $N$ noisy measurements. What are fundamental limits on the accuracy of parameter inference, given finite signal-to-noise…

Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…

We consider the estimation of a sparse parameter vector from measurements corrupted by white Gaussian noise. Our focus is on unbiased estimation as a setting under which the difficulty of the problem can be quantified analytically. We show…

Balanced truncation is a well-established model order reduction method which has been applied to a variety of problems. Recently, a connection between linear Gaussian Bayesian inference problems and the system-theoretic concept of balanced…

In this paper, we investigate the theoretical guarantees of penalized $\lun$ minimization (also called Basis Pursuit Denoising or Lasso) in terms of sparsity pattern recovery (support and sign consistency) from noisy measurements with…