Related papers: Support Recovery with Sparsely Sampled Free Random…
This paper addresses the statistical estimation of Gaussian Mixture Models (GMMs) with unknown diagonal covariances from independent and identically distributed samples. We employ the Beurling-LASSO (BLASSO), a convex optimization framework…
Low-cost message passing (MP) algorithm has been recognized as a promising technique for sparse vector recovery. However, the existing MP algorithms either focus on mean square error (MSE) of the value recovery while ignoring the sparsity…
Correlation between microstructure noise and latent financial logarithmic returns is an empirically relevant phenomenon with sound theoretical justification. With few notable exceptions, all integrated variance estimators proposed in the…
We analyze the performance of the least absolute shrinkage and selection operator (Lasso) for the linear model when the number of regressors $N$ grows larger keeping the true support size $d$ finite, i.e., the ultra-sparse case. The result…
Tremendous efforts have been made to study the theoretical and algorithmic aspects of sparse recovery and low-rank matrix recovery. This paper fills a theoretical gap in matrix recovery: the optimal sample complexity for stable recovery…
Tremendous efforts have been made to study the theoretical and algorithmic aspects of sparse recovery and low-rank matrix recovery. This paper fills a theoretical gap in matrix recovery: the optimal sample complexity for stable recovery…
Joint sparsity has attracted considerable attention in recent years in many fields including sparse signal recovery in compressed sensing (CS), statistics, and machine learning. Traditional convex models suffer from the suboptimal…
We consider the problem of recovering a structured signal $\mathbf{x} \in \mathbb{R}^{n}$ from noisy linear observations $\mathbf{y} =\mathbf{M} \mathbf{x}+\mathbf{w}$. The measurement matrix is modeled as $\mathbf{M} =…
We provide guarantees for learning latent variable models emphasizing on the overcomplete regime, where the dimensionality of the latent space can exceed the observed dimensionality. In particular, we consider multiview mixtures, spherical…
We consider the problem of recovering $n$ i.i.d samples from a zero mean multivariate Gaussian distribution with an unknown covariance matrix, from their modulo wrapped measurements, i.e., measurement where each coordinate is reduced modulo…
A noisy underdetermined system of linear equations is considered in which a sparse vector (a vector with a few nonzero elements) is subject to measurement. The measurement matrix elements are drawn from a Gaussian distribution. We study the…
Low-rank matrix recovery problems involving high-dimensional and heterogeneous data appear in applications throughout statistics and machine learning. The contribution of this paper is to establish the fundamental limits of recovery for a…
Recovery of support of a sparse vector from simple measurements is a widely-studied problem, considered under the frameworks of compressed sensing, 1-bit compressed sensing, and more general single index models. We consider generalizations…
In the problem of multiple support recovery, we are given access to linear measurements of multiple sparse samples in $\mathbb{R}^{d}$. These samples can be partitioned into $\ell$ groups, with samples having the same support belonging to…
We study the sample complexity of Bayesian recovery for solving inverse problems with general prior, forward operator and noise distributions. We consider posterior sampling according to an approximate prior $\mathcal{P}$, and establish…
We prove that iid random vectors that satisfy a rather weak moment assumption can be used as measurement vectors in Compressed Sensing, and the number of measurements required for exact reconstruction is the same as the best possible…
We consider the problem of exact support recovery of sparse signals via noisy measurements. The main focus is the sufficient and necessary conditions on the number of measurements for support recovery to be reliable. By drawing an analogy…
We study the problem of exact support recovery based on noisy observations and present Refined Least Squares (RLS). Given a set of noisy measurement $$ \myvec{y} = \myvec{X}\myvec{\theta}^* + \myvec{\omega},$$ and $\myvec{X} \in…
Bayesian hierarchical models have been demonstrated to provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models comprise typically a conditionally Gaussian prior model for the unknown, augmented by…
We study the information-theoretic limits of exactly recovering the support of a sparse signal using noisy projections defined by various classes of measurement matrices. Our analysis is high-dimensional in nature, in which the number of…