Related papers: Discrete uncertainty principles and sparse signal …

The characteristic functional is the infinite-dimensional generalization of the Fourier transform for measures on function spaces. It characterizes the statistical law of the associated stochastic process in the same way as a characteristic…

Sparse coding is a crucial subroutine in algorithms for various signal processing, deep learning, and other machine learning applications. The central goal is to learn an overcomplete dictionary that can sparsely represent a given input…

Block sparsity is an important parameter in many algorithms to successfully recover block sparse signals under the framework of compressive sensing. However, it is often unknown and needs to be estimated. Recently there emerges a few…

Uncertainty sampling, a popular active learning algorithm, is used to reduce the amount of data required to learn a classifier, but it has been observed in practice to converge to different parameters depending on the initialization and…

Neural networks and other machine learning models compute continuous representations, while humans communicate mostly through discrete symbols. Reconciling these two forms of communication is desirable for generating human-readable…

Uncertainty estimation has been widely studied in medical image segmentation as a tool to provide reliability, particularly in deep learning approaches. However, previous methods generally lack effective supervision in uncertainty…

A novel method to propagate uncertainty through the soft-thresholding nonlinearity is proposed in this paper. At every layer the current distribution of the target vector is represented as a spike and slab distribution, which represents the…

Privacy-protected microdata are often the desired output of a differentially private algorithm since microdata is familiar and convenient for downstream users. However, there is a statistical price for this kind of convenience. We show that…

This paper provides a new tractable lower bound for the sparse recovery threshold of sensing matrices. This lower bound is used as a proxy to quantify the quality of sensing matrices in two different applications. First, it serves as…

We develop a robust uncertainty principle for finite signals in C^N which states that for almost all subsets T,W of {0,...,N-1} such that |T|+|W| ~ (log N)^(-1/2) N, there is no sigal f supported on T whose discrete Fourier transform is…

Neural network models are widely used in solving many challenging problems, such as computer vision, personalized recommendation, and natural language processing. Those models are very computationally intensive and reach the hardware limit…

Detection of sparse signals arises in a wide range of modern scientific studies. The focus so far has been mainly on Gaussian mixture models. In this paper, we consider the detection problem under a general sparse mixture model and obtain…

This paper provides an extension of compressed sensing which bridges a substantial gap between existing theory and its current use in real-world applications. It introduces a mathematical framework that generalizes the three standard…

We study full Bayesian procedures for sparse linear regression when errors have a symmetric but otherwise unknown distribution. The unknown error distribution is endowed with a symmetrized Dirichlet process mixture of Gaussians. For the…

Many social and other networks exhibit stable size scaling relationships, such that features such as mean degree or reciprocation rates change slowly or are approximately constant as the number of vertices increases. Statistical network…

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…

This paper describes a novel technique for promoting sparsity in the modified filtered-x algorithms required for active noise control. The proposed algorithms are based on recent techniques incorporating approximations to the \ell_0-norm in…

We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to the…

In this paper we review the Heisenberg uncertainty principle in a discrete setting and, as in the classical uncertainty principle, we give it a dynamical sense related to the discrete Schr\"odinger equation. We study the convergence of the…

In this paper, we study the support recovery guarantees of underdetermined sparse regression using the $\ell_1$-norm as a regularizer and a non-smooth loss function for data fidelity. More precisely, we focus in detail on the cases of…