Related papers: Sharp thresholds for high-dimensional and noisy re…

Using a Bayesian approach, we consider the problem of recovering sparse signals under additive sparse and dense noise. Typically, sparse noise models outliers, impulse bursts or data loss. To handle sparse noise, existing methods…

Deepening and widening convolutional neural networks (CNNs) significantly increases the number of trainable weight parameters by adding more convolutional layers and feature maps per layer, respectively. By imposing inter- and intra-group…

We study the graph matching problem in the presence of vertex feature information using shallow graph neural networks. Specifically, given two graphs that are independent perturbations of a single random geometric graph with sparse binary…

This paper studies the problem of shuffled linear regression, where the correspondence between predictors and responses in a linear model is obfuscated by a latent permutation. Specifically, we consider the model $y = \Pi_* X \beta_* + w$,…

Most compressed sensing algorithms do not account for the effect of saturation in noisy compressed measurements, though saturation is an important consequence of the limited dynamic range of existing sensors. The few algorithms that handle…

Our work is focused on the joint sparsity recovery problem where the common sparsity pattern is corrupted by Poisson noise. We formulate the confidence-constrained optimization problem in both least squares (LS) and maximum likelihood (ML)…

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…

We investigate non-negative least squares (NNLS) for the recovery of sparse non-negative vectors from noisy linear and biased measurements. We build upon recent results from [1] showing that for matrices whose row-span intersects the…

We propose a new method for reconstruction of sparse signals with and without noisy perturbations, termed the subspace pursuit algorithm. The algorithm has two important characteristics: low computational complexity, comparable to that of…

We study a generalized framework for structured sparsity. It extends the well-known methods of Lasso and Group Lasso by incorporating additional constraints on the variables as part of a convex optimization problem. This framework provides…

We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…

The problem of detecting the sparsity pattern of a k-sparse vector in R^n from m random noisy measurements is of interest in many areas such as system identification, denoising, pattern recognition, and compressed sensing. This paper…

We study the support recovery problem for compressed sensing, where the goal is to reconstruct the a high-dimensional $K$-sparse signal $\mathbf{x}\in\mathbb{R}^N$, from low-dimensional linear measurements with and without noise. Our key…

The sparse group Lasso is a widely used statistical model which encourages the sparsity both on a group and within the group level. In this paper, we develop an efficient augmented Lagrangian method for large-scale non-overlapping sparse…

We study verifiable sufficient conditions and computable performance bounds for sparse recovery algorithms such as the Basis Pursuit, the Dantzig selector and the Lasso estimator, in terms of a newly defined family of quality measures for…

We consider the problem of fitting the parameters of a high-dimensional linear regression model. In the regime where the number of parameters $p$ is comparable to or exceeds the sample size $n$, a successful approach uses an…

In Gaussian graphical model selection, noise-corrupted samples present significant challenges. It is known that even minimal amounts of noise can obscure the underlying structure, leading to fundamental identifiability issues. A recent line…

In this article, we discuss a novel greedy algorithm for the recovery of compressive sampled signals under noisy conditions. Most of the greedy recovery algorithms proposed in the literature require sparsity of the signal to be known or…

Consider estimating a structured signal $\mathbf{x}_0$ from linear, underdetermined and noisy measurements $\mathbf{y}=\mathbf{A}\mathbf{x}_0+\mathbf{z}$, via solving a variant of the lasso algorithm: $\hat{\mathbf{x}}=\arg\min_\mathbf{x}\{…

We study a sample complexity vs. conditioning tradeoff in modern signal recovery problems (including sparse recovery, low-rank matrix sensing, covariance estimation, and abstract phase retrieval), where convex optimization problems are…