Related papers: Limits on Support Recovery with Probabilistic Mode…
Consider the compressed sensing setup where the support $s^*$ of an $m$-sparse $d$-dimensional signal $x$ is to be recovered from $n$ linear measurements with a given algorithm. Suppose that the measurements are such that the algorithm does…
This note presents a unified analysis of the recovery of simple objects from random linear measurements. When the linear functionals are Gaussian, we show that an s-sparse vector in R^n can be efficiently recovered from 2s log n…
Orthogonal Matching pursuit (OMP) is a popular algorithm to estimate an unknown sparse vector from multiple linear measurements of it. Assuming exact sparsity and that the measurements are corrupted by additive Gaussian noise, the success…
The sample compression theory provides generalization guarantees for predictors that can be fully defined using a subset of the training dataset and a (short) message string, generally defined as a binary sequence. Previous works provided…
Multi-view data arises frequently in modern network analysis e.g. relations of multiple types among individuals in social network analysis, longitudinal measurements of interactions among observational units, annotated networks with noisy…
Known sparsity thresholds for basis pursuit to deliver the maximally sparse solution of the compressed sensing recovery problem typically depend on the dictionary's coherence. While the coherence is easy to compute, it can lead to rather…
We study the problem of consistently recovering the sparsity pattern of a regression parameter vector from correlated observations governed by deterministic missing data patterns using Lasso. We consider the case in which the observed…
We address the problem of joint sparsity pattern recovery based on low dimensional multiple measurement vectors (MMVs) in resource constrained distributed networks. We assume that distributed nodes observe sparse signals which share the…
Recovering an unknown but structured signal from its measurements is a challenging problem with significant applications in fields such as imaging restoration, wireless communications, and signal processing. In this paper, we consider the…
The choice of the sensing matrix is crucial in compressed sensing. Random Gaussian sensing matrices satisfy the restricted isometry property, which is crucial for solving the sparse recovery problem using convex optimization techniques.…
This paper investigates the problem of signal estimation from undersampled noisy sub-Gaussian measurements under the assumption of a cosparse model. Based on generalized notions of sparsity, we derive novel recovery guarantees for the…
We study the problem of recovering a block-sparse signal from under-sampled observations. The non-zero values of such signals appear in few blocks, and their recovery is often accomplished using a $\ell_{1,2}$ optimization problem. In…
Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and…
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…
Decision trees are widely used for their low computational cost, good predictive performance, and ability to assess the importance of features. Though often used in practice for feature selection, the theoretical guarantees of these methods…
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…
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…
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…
We consider approximation or recovery of functions based on a finite number of function evaluations. This is a well-studied problem in optimal recovery, machine learning, and numerical analysis in general, but many fundamental insights were…
The {\it straight-through estimator} (STE) is commonly used to optimize quantized neural networks, yet its contexts of effective performance are still unclear despite empirical successes.To make a step forward in this comprehension, we…