Related papers: Robust 1-bit compressed sensing and sparse logisti…

Traditional sampling theories consider the problem of reconstructing an unknown signal $x$ from a series of samples. A prevalent assumption which often guarantees recovery from the given measurements is that $x$ lies in a known subspace.…

One-bit compressed sensing (1bCS) is an extremely quantized signal acquisition method that has been proposed and studied rigorously in the past decade. In 1bCS, linear samples of a high dimensional signal are quantized to only one bit per…

We develop a technique to design efficiently computable estimators for sparse linear regression in the simultaneous presence of two adversaries: oblivious and adaptive. We design several robust algorithms that outperform the state of the…

Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…

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…

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…

Compressed sensing aims at reconstructing sparse signals from significantly reduced number of samples, and a popular reconstruction approach is $\ell_1$-norm minimization. In this correspondence, a method called orthonormal expansion is…

We study the problem of estimation and testing in logistic regression with class-conditional noise in the observed labels, which has an important implication in the Positive-Unlabeled (PU) learning setting. With the key observation that the…

We consider the recovery of a nonnegative vector x from measurements y = Ax, where A is an m-by-n matrix whos entries are in {0, 1}. We establish that when A corresponds to the adjacency matrix of a bipartite graph with sufficient…

We study the use of very sparse random projections for compressed sensing (sparse signal recovery) when the signal entries can be either positive or negative. In our setting, the entries of a Gaussian design matrix are randomly sparsified…

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…

We consider the stochastic approximation problem where a convex function has to be minimized, given only the knowledge of unbiased estimates of its gradients at certain points, a framework which includes machine learning methods based on…

The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…

We present a sparse analogue to stochastic gradient descent that is guaranteed to perform well under similar conditions to the lasso. In the linear regression setup with irrepresentable noise features, our algorithm recovers the support set…

In this paper, we consider a compressed sensing problem of reconstructing a sparse signal from an undersampled set of noisy linear measurements. The regularized least squares or least absolute shrinkage and selection operator (LASSO)…

One-bit measurements widely exist in the real world, and they can be used to recover sparse signals. This task is known as the problem of learning halfspaces in learning theory and one-bit compressive sensing (1bit-CS) in signal processing.…

Compressive sensing aims to recover a high-dimensional sparse signal from a relatively small number of measurements. In this paper, a novel design of the measurement matrix is proposed. The design is inspired by the construction of…

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…

In presence of sparse noise we propose kernel regression for predicting output vectors which are smooth over a given graph. Sparse noise models the training outputs being corrupted either with missing samples or large perturbations. The…

Linear encoding of sparse vectors is widely popular, but is commonly data-independent -- missing any possible extra (but a priori unknown) structure beyond sparsity. In this paper we present a new method to learn linear encoders that adapt…