Related papers: Signal recovery by Stochastic Optimization
We propose two novel approaches to the recovery of an (approximately) sparse signal from noisy linear measurements in the case that the signal is a priori known to be non-negative and obey given linear equality constraints, such as simplex…
We consider the problem of recovering linear image $Bx$ of a signal $x$ known to belong to a given convex compact set $X$ from indirect observation $\omega=Ax+\sigma\xi$ of $x$ corrupted by Gaussian noise $\xi$. It is shown that under some…
This paper re-visits the spectral method for learning latent variable models defined in terms of observable operators. We give a new perspective on the method, showing that operators can be recovered by minimizing a loss defined on a finite…
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…
We study the task of learning Generalized Linear models (GLMs) in the agnostic model under the Gaussian distribution. We give the first polynomial-time algorithm that achieves a constant-factor approximation for \textit{any} monotone…
In this paper, we present a novel stochastic method for solving variational inequalities (VI) in the context of Markovian noise. By leveraging Extragradient technique, we can productively solve VI optimization problems characterized by…
We consider the problem of learning mixtures of generalized linear models (GLM) which arise in classification and regression problems. Typical learning approaches such as expectation maximization (EM) or variational Bayes can get stuck in…
We study phase retrieval from magnitude measurements of an unknown signal as an algebraic estimation problem. Indeed, phase retrieval from rank-one and more general linear measurements can be treated in an algebraic way. It is verified that…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
In this work, we investigate an efficient numerical approach for solving higher order statistical methods for blind and semi-blind signal recovery from non-ideal channels. We develop numerical algorithms based on convex optimization…
Recent advances in quantized compressed sensing and high-dimensional estimation have shown that signal recovery is even feasible under strong non-linear distortions in the observation process. An important characteristic of associated…
We provide a new methodology for statistical recovery of single linear mixtures of piecewise constant signals (sources) with unknown mixing weights and change points in a multiscale fashion. We show exact recovery within an…
We consider the problem of reconstructing a signal from multi-layered (possibly) non-linear measurements. Using non-rigorous but standard methods from statistical physics we present the Multi-Layer Approximate Message Passing (ML-AMP)…
We propose a method to reconstruct sparse signals degraded by a nonlinear distortion and acquired at a limited sampling rate. Our method formulates the reconstruction problem as a nonconvex minimization of the sum of a data fitting term and…
We introduce a new computational framework for estimating parameters in generalized generalized linear models (GGLM), a class of models that extends the popular generalized linear models (GLM) to account for dependencies among observations…
This paper presents a novel value iteration (VI) algorithm for finding the optimal control for a kind of infinite-horizon stochastic linear quadratic (SLQ) problem with unknown systems. First, an off-line algorithm is estabilished to obtain…
We consider the problem of parameter estimation from a generalized linear model with a random design matrix that is orthogonally invariant in law. Such a model allows the design have an arbitrary distribution of singular values and only…
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…
Signal retrieval from a series of indirect measurements is a common task in many imaging, metrology and characterization platforms in science and engineering. Because most of the indirect measurement processes are well-described by physical…
We discuss the approach to estimate aggregation and adaptive estimation based upon (nearly optimal) testing of convex hypotheses. We show that in the situation where the observations stem from {\em simple observation schemes} and where set…