Related papers: Support Recovery with Sparsely Sampled Free Random…

In the noisy population recovery problem of Dvir et al., the goal is to learn an unknown distribution $f$ on binary strings of length $n$ from noisy samples. For some parameter $\mu \in [0,1]$, a noisy sample is generated by flipping each…

We consider the problem of learning a coefficient vector x_0\in R^N from noisy linear observation y=Ax_0+w \in R^n. In many contexts (ranging from model selection to image processing) it is desirable to construct a sparse estimator x'. In…

We extend the theory of low-rank matrix recovery and completion to the case when Poisson observations for a linear combination or a subset of the entries of a matrix are available, which arises in various applications with count data. We…

Gaussian process regression in its most simplified form assumes normal homoscedastic noise and utilizes analytically tractable mean and covariance functions of predictive posterior distribution using Gaussian conditioning. Its…

There are two major routes to address the ubiquitous family of inverse problems appearing in signal and image processing, such as denoising or deblurring. A first route relies on Bayesian modeling, where prior probabilities are used to…

We consider estimation models of the form $Y=X^*+N$, where $X^*$ is some $m$-dimensional signal we wish to recover, and $N$ is symmetrically distributed noise that may be unbounded in all but a small $\alpha$ fraction of the entries. We…

We analyze the asymptotic performance of sparse signal recovery from noisy measurements. In particular, we generalize some of the existing results for the Gaussian case to subgaussian and other ensembles. An achievable result is presented…

In this paper we consider the problem of linear unmixing hidden random variables defined over the simplex with additive Gaussian noise, also known as probabilistic simplex component analysis (PRISM). Previous solutions to tackle this…

The central problem we address in this work is estimation of the parameter support set S, the set of indices corresponding to nonzero parameters, in the context of a sparse parametric likelihood model for discrete multivariate time series.…

We propose a new Bayesian Neural Net formulation that affords variational inference for which the evidence lower bound is analytically tractable subject to a tight approximation. We achieve this tractability by (i) decomposing ReLU…

We propose a robust and efficient approach to the problem of compressive phase retrieval in which the goal is to reconstruct a sparse vector from the magnitude of a number of its linear measurements. The proposed framework relies on…

We consider the problem of learning a graph modeling the statistical relations of the $d$ variables from a dataset with $n$ samples $X \in \mathbb{R}^{n \times d}$. Standard approaches amount to searching for a precision matrix $\Theta$…

The field of compressed sensing has become a major tool in high-dimensional analysis, with the realization that vectors can be recovered from relatively very few linear measurements as long as the vectors lie in a low-dimensional structure,…

We consider the problem of estimating complex statistical latent variable models using variational Bayes methods. These methods are used when exact posterior inference is either infeasible or computationally expensive, and they approximate…

In this work, we study scaling limits of shallow Bayesian neural networks (BNNs) via their connection to Gaussian processes (GPs), with an emphasis on statistical modeling, identifiability, and scalable inference. We first establish a…

The problem of population recovery refers to estimating a distribution based on incomplete or corrupted samples. Consider a random poll of sample size $n$ conducted on a population of individuals, where each pollee is asked to answer $d$…

We obtain estimation error rates for estimators obtained by aggregation of regularized median-of-means tests, following a construction of Le Cam. The results hold with exponentially large probability -- as in the gaussian framework with…

Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. Structure present in these problems allows efficient optimization strategies - a well known example is…

We derive fundamental sample complexity bounds for recovering sparse and structured signals for linear and nonlinear observation models including sparse regression, group testing, multivariate regression and problems with missing features.…

We study the problem of jointly sparse support recovery with 1-bit compressive measurements in a sensor network. Sensors are assumed to observe sparse signals having the same but unknown sparse support. Each sensor quantizes its measurement…