Related papers: Compressive Recovery of Sparse Precision Matrices

We apply a method recently introduced to the statistical literature to directly estimate the precision matrix from an ensemble of samples drawn from a corresponding Gaussian distribution. Motivated by the observation that cosmological…

The Graphical Lasso (GLasso) algorithm is fast and widely used for estimating sparse precision matrices (Friedman et al., 2008). Its central role in the literature of high-dimensional covariance estimation rivals that of Lasso regression…

In Compressed Sensing, a real-valued sparse vector has to be estimated from an underdetermined system of linear equations. In many applications, however, the elements of the sparse vector are drawn from a finite set. For the estimation of…

We propose maximum likelihood estimation for learning Gaussian graphical models with a Gaussian (ell_2^2) prior on the parameters. This is in contrast to the commonly used Laplace (ell_1) prior for encouraging sparseness. We show that our…

We consider the problem of the recovery of a k-sparse vector from compressed linear measurements when data are corrupted by a quantization noise. When the number of measurements is not sufficiently large, different $k$-sparse solutions may…

In this paper, we consider the mixture of sparse linear regressions model. Let ${\beta}^{(1)},\ldots,{\beta}^{(L)}\in\mathbb{C}^n$ be $ L $ unknown sparse parameter vectors with a total of $ K $ non-zero coefficients. Noisy linear…

The recovery of sparsest overcomplete representation has recently attracted intensive research activities owe to its important potential in the many applied fields such as signal processing, medical imaging, communication, and so on. This…

Classical results in sparse recovery guarantee the exact reconstruction of $s$-sparse signals under assumptions on the dictionary that are either too strong or NP-hard to check. Moreover, such results may be pessimistic in practice since…

Estimation of a high dimensional precision matrix is a critical problem to many areas of statistics including Gaussian graphical models and inference on high dimensional data. Working under the structural assumption of sparsity, we propose…

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…

We consider the problem of learning a conditional Gaussian graphical model in the presence of latent variables. Building on recent advances in this field, we suggest a method that decomposes the parameters of a conditional Markov random…

Compressed sensing is a relatively new mathematical paradigm that shows a small number of linear measurements are enough to efficiently reconstruct a large dimensional signal under the assumption the signal is sparse. Applications for this…

Matrix recovery from sparse observations is an extensively studied topic emerging in various applications, such as recommendation system and signal processing, which includes the matrix completion and compressed sensing models as special…

In this paper, we propose a general framework for sparse and low-rank tensor estimation from cubic sketchings. A two-stage non-convex implementation is developed based on sparse tensor decomposition and thresholded gradient descent, which…

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…

Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…

We propose a novel algorithm for efficiently computing a sparse directed adjacency matrix from a group of time series following a causal graph process. Our solution is scalable for both dense and sparse graphs and automatically selects the…

For a tall $n\times d$ matrix $A$ and a random $m\times n$ sketching matrix $S$, the sketched estimate of the inverse covariance matrix $(A^\top A)^{-1}$ is typically biased: $E[(\tilde A^\top\tilde A)^{-1}]\ne(A^\top A)^{-1}$, where…

Auto-Encoders are unsupervised models that aim to learn patterns from observed data by minimizing a reconstruction cost. The useful representations learned are often found to be sparse and distributed. On the other hand, compressed sensing…

Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical…