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Related papers: A unifying tutorial on Approximate Message Passing

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We consider the problem of estimating a signal from measurements obtained via a generalized linear model. We focus on estimators based on approximate message passing (AMP), a family of iterative algorithms with many appealing features: the…

Machine Learning · Statistics 2021-02-18 Marco Mondelli , Ramji Venkataramanan

Motivated by the recent application of approximate message passing (AMP) to the analysis of convex optimizations in multi-class classifications [Loureiro, et. al., 2021], we present a convergence analysis of AMP dynamics with non-separable…

Machine Learning · Computer Science 2024-02-14 Burak Çakmak , Yue M. Lu , Manfred Opper

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…

Signal Processing · Electrical Eng. & Systems 2024-07-26 Jun Lu , Lei Liu , Shunqi Huang , Ning Wei , Xiaoming Chen

Approximate message passing (AMP) methods have gained recent traction in sparse signal recovery. Additional information about the signal, or \emph{side information} (SI), is commonly available and can aid in efficient signal recovery. This…

Information Theory · Computer Science 2019-05-06 Anna Ma , You , Zhou , Cynthia Rush , Dror Baron , Deanna Needell

Approximate message passing (AMP) is a class of low-complexity, scalable algorithms for solving high-dimensional linear regression tasks where one wishes to recover an unknown signal from noisy, linear measurements. AMP is an iterative…

Information Theory · Computer Science 2019-08-27 Yanting Ma , Cynthia Rush , Dror Baron

We consider a class of approximated message passing (AMP) algorithms and characterize their high-dimensional behavior in terms of a suitable state evolution recursion. Our proof applies to Gaussian matrices with independent but not…

Probability · Mathematics 2013-01-01 Adel Javanmard , Andrea Montanari

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…

Machine Learning · Statistics 2022-12-06 Yizhou Xu , TianQi Hou , ShanSuo Liang , Marco Mondelli

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…

Statistics Theory · Mathematics 2019-08-08 Andrea Montanari , Ramji Venkataramanan

Approximate message passing algorithm enjoyed considerable attention in the last decade. In this paper we introduce a variant of the AMP algorithm that takes into account glassy nature of the system under consideration. We coin this…

Disordered Systems and Neural Networks · Physics 2019-02-07 Fabrizio Antenucci , Florent Krzakala , Pierfrancesco Urbani , Lenka Zdeborová

Approximate message passing (AMP) has emerged both as a popular class of iterative algorithms and as a powerful analytic tool in a wide range of statistical estimation problems and statistical physics models. A well established line of AMP…

Statistics Theory · Mathematics 2025-07-22 Zhigang Bao , Qiyang Han , Xiaocong Xu

Message-passing (MP) is a powerful tool for finding an approximate solution in optimization. We generalize it to nonlinear product-sum form, and numerically show the fast convergence for the minimum feedback vertex set and the minimum…

Physics and Society · Physics 2024-04-03 Yukio Hayashi

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…

Data Structures and Algorithms · Computer Science 2024-11-06 Misha Ivkov , Tselil Schramm

We introduce a theoretical approach for designing generalizations of the approximate message passing (AMP) algorithm for compressed sensing which are valid for large observation matrices that are drawn from an invariant random matrix…

Information Theory · Computer Science 2017-05-12 Burak Çakmak , Manfred Opper , Ole Winther , Bernard H. Fleury

In this paper, we present structured message passing (SMP), a unifying framework for approximate inference algorithms that take advantage of structured representations such as algebraic decision diagrams and sparse hash tables. These…

Artificial Intelligence · Computer Science 2013-09-27 Vibhav Gogate , Pedro Domingos

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…

Machine Learning · Statistics 2024-04-10 Nelvin Tan , Ramji Venkataramanan

This paper is divided into two parts. The first part is devoted to the study of a class of Approximate Message Passing (AMP) algorithms which are widely used in the fields of statistical physics, machine learning, or communication theory.…

Probability · Mathematics 2024-06-13 Walid Hachem

Approximate message passing (AMP) is a scalable, iterative approach to signal recovery. For structured random measurement ensembles, including independent and identically distributed (i.i.d.) Gaussian and rotationally-invariant matrices,…

Information Theory · Computer Science 2023-06-27 Dang Qua Nguyen , Taejoon Kim

We consider the problem of decoding a discrete signal of categorical variables from the observation of several histograms of pooled subsets of it. We present an Approximate Message Passing (AMP) algorithm for recovering the signal in the…

Information Theory · Computer Science 2020-01-22 Ahmed El Alaoui , Aaditya Ramdas , Florent Krzakala , Lenka Zdeborova , Michael I. Jordan

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…

Information Theory · Computer Science 2015-06-17 Jason T. Parker , Philip Schniter , Volkan Cevher

For certain sensing matrices, the Approximate Message Passing (AMP) algorithm efficiently reconstructs undersampled signals. However, in Magnetic Resonance Imaging (MRI), where Fourier coefficients of a natural image are sampled with…

Signal Processing · Electrical Eng. & Systems 2020-09-08 Charles Millard , Aaron T Hess , Boris Mailhé , Jared Tanner