Related papers: Fixed Points of Generalized Approximate Message Pa…
High-dimensional signal recovery of standard linear regression is a key challenge in many engineering fields, such as, communications, compressed sensing, and image processing. The approximate message passing (AMP) algorithm proposed by…
We study the problem of regression in a generalized linear model (GLM) with multiple signals and latent variables. This model, which we call a matrix GLM, covers many widely studied problems in statistical learning, including mixed linear…
Approximate message passing (AMP) algorithms are devised under the Gaussianity assumption of the measurement noise vector. In this work, we relax this assumption within the vector AMP (VAMP) framework to arbitrary independent and…
Over the last decade or so, Approximate Message Passing (AMP) algorithms have become extremely popular in various structured high-dimensional statistical problems. The fact that the origins of these techniques can be traced back to notions…
Conformal prediction has emerged as a powerful tool for building prediction intervals that are valid in a distribution-free way. However, its evaluation may be computationally costly, especially in the high-dimensional setting where the…
We extend the generalized approximate message passing (G-AMP) approach, originally proposed for high-dimensional generalized-linear regression in the context of compressive sensing, to the generalized-bilinear case, which enables its…
We consider the problem of reconstructing the signal and the hidden variables from observations coming from a multi-layer network with rotationally invariant weight matrices. The multi-layer structure models inference from deep generative…
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…
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…
We give a fast, spectral procedure for implementing approximate-message passing (AMP) algorithms robustly. For any quadratic optimization problem over symmetric matrices $X$ with independent subgaussian entries, and any separable AMP…
Approximate message passing (AMP) algorithms are iterative methods for signal recovery in noisy linear systems. In some scenarios, AMP algorithms need to operate within a distributed network. To address this challenge, the distributed…
Approximate Message Passing (AMP) is a class of iterative algorithms that have found applications in many problems in high-dimensional statistics and machine learning. In its general form, AMP can be formulated as an iterative procedure…
Decentralized generalized approximate message-passing (GAMP) is proposed for compressed sensing from distributed generalized linear measurements in a tree-structured network. Consensus propagation is used to realize average consensus…
Approximate message passing (AMP) and its variants, developed based on loopy belief propagation, are attractive for estimating a vector x from a noisy version of z = Ax, which arises in many applications. For a large A with i. i. d.…
For the problem of binary linear classification and feature selection, we propose algorithmic approaches to classifier design based on the generalized approximate message passing (GAMP) algorithm, recently proposed in the context of…
Approximate Message Passing (AMP), originally designed to solve high-dimensional linear inverse problems, has found broad applications in signal processing and statistical inference. Among its key variants, Vector Approximate Message…
This paper considers a discrete-valued signal estimation scheme based on a low-complexity Bayesian optimal message passing algorithm (MPA) for solving massive linear inverse problems under highly correlated measurements. Gaussian belief…
Generalized Linear Models (GLMs), where a random vector $\mathbf{x}$ is observed through a noisy, possibly nonlinear, function of a linear transform $\mathbf{z}=\mathbf{Ax}$ arise in a range of applications in nonlinear filtering and…
A concise expectation propagation (EP) based message passing algorithm (MPA) is derived for the general measurement channel. By neglecting some high-order infinitesimal terms, the EP-MPA is proven to be equivalent to the Generalized…
Approximate message passing (AMP) is a family of iterative algorithms that generalize matrix power iteration. AMP algorithms are known to optimally solve many average-case optimization problems. In this paper, we show that a large class of…