Related papers: Message-passing algorithms for synchronization pro…
Consider the problem of estimating a low-rank matrix when its entries are perturbed by Gaussian noise. If the empirical distribution of the entries of the spikes is known, optimal estimators that exploit this knowledge can substantially…
Gaussian and quadratic approximations of message passing algorithms on graphs have attracted considerable recent attention due to their computational simplicity, analytic tractability, and wide applicability in optimization and statistical…
The ubiquity of approximately sparse data has led a variety of com- munities to great interest in compressed sensing algorithms. Although these are very successful and well understood for linear measurements with additive noise, applying…
We propose and analyze an approximate message passing (AMP) algorithm for the matrix tensor product model, which is a generalization of the standard spiked matrix models that allows for multiple types of pairwise observations over a…
We consider a group synchronization problem with multiple frequencies which involves observing pairwise relative measurements of group elements on multiple frequency channels, corrupted by Gaussian noise. We study the computational phase…
Approximate Message Passing (AMP) has been shown to be a superior method for inference problems, such as the recovery of signals from sets of noisy, lower-dimensionality measurements, both in terms of reconstruction accuracy and in…
Approximate message passing (AMP) refers to a class of efficient algorithms for statistical estimation in high-dimensional problems such as compressed sensing and low-rank matrix estimation. This paper analyzes the performance of AMP in the…
In the pooled data problem, the goal is to identify the categories associated with a large collection of items via a sequence of pooled tests. Each pooled test reveals the number of items of each category within the pool. We study an…
Network alignment generalizes and unifies several approaches for forming a matching or alignment between the vertices of two graphs. We study a mathematical programming framework for network alignment problem and a sparse variation of it…
We study the computational phase transition in a multi-frequency group synchronization problem, where pairwise relative measurements of group elements are observed across multiple frequency channels and corrupted by Gaussian noise. Using…
We propose an efficient algorithm for solving group synchronization under high levels of corruption and noise, while we focus on rotation synchronization. We first describe our recent theoretically guaranteed message passing algorithm that…
In a recent paper, the authors proposed a new class of low-complexity iterative thresholding algorithms for reconstructing sparse signals from a small set of linear measurements \cite{DMM}. The new algorithms are broadly referred to as AMP,…
With a unified belief propagation (BP) and mean field (MF) framework, we propose an iterative message passing receiver, which performs joint channel state and noise precision (the reciprocal of noise variance) estimation and decoding for…
We study the compressed sensing reconstruction problem for a broad class of random, band-diagonal sensing matrices. This construction is inspired by the idea of spatial coupling in coding theory. As demonstrated heuristically and…
We consider the estimation of an i.i.d.\ random vector observed through a linear transform followed by a componentwise, probabilistic (possibly nonlinear) measurement channel. A novel algorithm, called generalized approximate message…
The problem of estimating a random vector x from noisy linear measurements y = A x + w with unknown parameters on the distributions of x and w, which must also be learned, arises in a wide range of statistical learning and linear inverse…
Estimation of a vector from quantized linear measurements is a common problem for which simple linear techniques are suboptimal -- sometimes greatly so. This paper develops generalized approximate message passing (GAMP) algorithms for…
We propose a novel formulation for phase synchronization -- the statistical problem of jointly estimating alignment angles from noisy pairwise comparisons -- as a nonconvex optimization problem that enforces consistency among the pairwise…
In a recent paper, the authors proposed a new class of low-complexity iterative thresholding algorithms for reconstructing sparse signals from a small set of linear measurements \cite{DMM}. The new algorithms are broadly referred to as AMP,…
This paper is concerned with the problem of reconstructing an unknown rank-one matrix with prior structural information from noisy observations. While computing the Bayes-optimal estimator seems intractable in general due to its nonconvex…