Related papers: Support Recovery with Sparsely Sampled Free Random…

To adopt neural networks in safety critical domains, knowing whether we can trust their predictions is crucial. Bayesian neural networks (BNNs) provide uncertainty estimates by averaging predictions with respect to the posterior weight…

Sparse recovery from linear Gaussian measurements has been the subject of much investigation since the breaktrough papers \cite{CRT:IEEEIT06} and \cite{donoho2006compressed} on Compressed Sensing. Application to sparse vectors and sparse…

We present a new theoretical perspective of data noising in recurrent neural network language models (Xie et al., 2017). We show that each variant of data noising is an instance of Bayesian recurrent neural networks with a particular…

We give a new approach to the dictionary learning (also known as "sparse coding") problem of recovering an unknown $n\times m$ matrix $A$ (for $m \geq n$) from examples of the form \[ y = Ax + e, \] where $x$ is a random vector in $\mathbb…

Data dispersed across multiple files are commonly integrated through probabilistic linkage methods, where even minimal error rates in record matching can significantly contaminate subsequent statistical analyses. In regression problems, we…

Sparse recovery in linear systems underpins applications from signal processing to high-dimensional regression. Sparse Bayesian Learning, grounded in the principle of automatic relevance determination (ARD), offers a practical Bayesian…

In multivariate regression, a $K$-dimensional response vector is regressed upon a common set of $p$ covariates, with a matrix $B^*\in\mathbb{R}^{p\times K}$ of regression coefficients. We study the behavior of the multivariate group Lasso,…

Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical…

Let $X_0$ be an unknown $M$ by $N$ matrix. In matrix recovery, one takes $n < MN$ linear measurements $y_1,..., y_n$ of $X_0$, where $y_i = \Tr(a_i^T X_0)$ and each $a_i$ is a $M$ by $N$ matrix. For measurement matrices with Gaussian i.i.d…

Many problems in statistics and machine learning require the reconstruction of a rank-one signal matrix from noisy data. Enforcing additional prior information on the rank-one component is often key to guaranteeing good recovery…

We study a class of real robust phase retrieval problems under a Gaussian assumption on the coding matrix when the received signal is sparsely corrupted by noise. The goal is to establish conditions on the sparsity under which the input…

In this paper, we propose a generalized scale mixture family of distributions, namely the Power Exponential Scale Mixture (PESM) family, to model the sparsity inducing priors currently in use for sparse signal recovery (SSR). We show that…

We study a statistical model for the tensor principal component analysis problem introduced by Montanari and Richard: Given a order-$3$ tensor $T$ of the form $T = \tau \cdot v_0^{\otimes 3} + A$, where $\tau \geq 0$ is a signal-to-noise…

In Gaussian graphical model selection, noise-corrupted samples present significant challenges. It is known that even minimal amounts of noise can obscure the underlying structure, leading to fundamental identifiability issues. A recent line…

We study variable selection (also called support recovery) in high-dimensional sparse linear regression when one has external information on which variables are likely to be associated with the response. Consistent recovery is only possible…

This paper develops a new empirical Bayesian inference algorithm for solving a linear inverse problem given multiple measurement vectors (MMV) of under-sampled and noisy observable data. Specifically, by exploiting the joint sparsity across…

We propose a rectangular rotational invariant estimator to recover a real matrix from noisy matrix observations coming from an arbitrary additive rotational invariant perturbation, in the large dimension limit. Using the Bayes-optimality of…

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…

In this paper, we develop a generalized Bayesian inference framework for a collection of signal-plus-noise matrix models arising in high-dimensional statistics and many applications. The framework is built upon an asymptotically unbiased…

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.…