Related papers: Compressed Sensing with Adversarial Sparse Noise v…
This paper proposes a sparse regression strategy for discovery of ordinary differential equations from incomplete and noisy data. Inference is performed over both equation parameters and state variables using a statistically motivated…
Reconstruction fidelity of sparse signals contaminated by sparse noise is considered. Statistical mechanics inspired tools are used to show that the l1-norm based convex optimization algorithm exhibits a phase transition between the…
We propose to reduce the original well-posed problem of compressive sensing to weighted-MAX-SAT. Compressive sensing is a novel randomized data acquisition approach that linearly samples sparse or compressible signals at a rate much below…
Noise robust compressive sensing algorithm is considered. This algorithm allows an efficient signal reconstruction in the presence of different types of noise due to the possibility to change minimization norm. For instance, the commonly…
Over the past years, there are increasing interests in recovering the signals from undersampling data where such signals are sparse under some orthogonal dictionary or tight framework, which is referred to be sparse synthetic model. More…
Convolutional sparse coding (CSC) can learn representative shift-invariant patterns from multiple kinds of data. However, existing CSC methods can only model noises from Gaussian distribution, which is restrictive and unrealistic. In this…
This paper studies the problem of secure state estimation of a linear time-invariant (LTI) system with bounded noise in the presence of sparse attacks on an unknown, time-varying set of sensors. In other words, at each time, the attacker…
The goal of compressed sensing is to estimate a vector from an underdetermined system of noisy linear measurements, by making use of prior knowledge on the structure of vectors in the relevant domain. For almost all results in this…
The sparse linear regression problem is difficult to handle with usual sparse optimization models when both predictors and measurements are either quantized or represented in low-precision, due to non-convexity. In this paper, we provide a…
In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…
Robust and sparse estimation of linear regression coefficients is investigated. The situation addressed by the present paper is that covariates and noises are sampled from heavy-tailed distributions, and the covariates and noises are…
We study the fundamental problem of ReLU regression, where the goal is to fit Rectified Linear Units (ReLUs) to data. This supervised learning task is efficiently solvable in the realizable setting, but is known to be computationally hard…
We propose an efficient optimization algorithm for selecting a subset of training data to induce sparsity for Gaussian process regression. The algorithm estimates an inducing set and the hyperparameters using a single objective, either the…
In high dimension, it is customary to consider Lasso-type estimators to enforce sparsity. For standard Lasso theory to hold, the regularization parameter should be proportional to the noise level, yet the latter is generally unknown in…
We consider the problem of multivariate regression in a setting where the relevant predictors could be shared among different responses. We propose an algorithm which decomposes the coefficient matrix into the product of a long matrix and a…
Noiseless compressive sensing is a protocol that enables undersampling and later recovery of a signal without loss of information. This compression is possible because the signal is usually sufficiently sparse in a given basis. Currently,…
One of the crucial tasks in many inference problems is the extraction of sparse information out of a given number of high-dimensional measurements. In machine learning, this is frequently achieved using, as a penality term, the $L_p$ norm…
We consider the estimation of a sparse parameter vector from measurements corrupted by white Gaussian noise. Our focus is on unbiased estimation as a setting under which the difficulty of the problem can be quantified analytically. We show…
Pruning the weights of neural networks is an effective and widely-used technique for reducing model size and inference complexity. We develop and test a novel method based on compressed sensing which combines the pruning and training into a…
Broadband frequency-selective fading channels usually have the inherent sparse nature. By exploiting the sparsity, adaptive sparse channel estimation (ASCE) algorithms, e.g., least mean square with reweighted L1-norm constraint (LMS-RL1)…