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We study a class of Approximate Message Passing (AMP) algorithms for symmetric and rectangular spiked random matrix models with orthogonally invariant noise. The AMP iterates have fixed dimension $K \geq 1$, a multivariate non-linearity is…

Statistics Theory · Mathematics 2024-06-14 Xinyi Zhong , Tianhao Wang , Zhou Fan

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

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

Approximate message passing (AMP) is a low-cost iterative parameter-estimation technique for certain high-dimensional linear systems with non-Gaussian distributions. However, AMP only applies to independent identically distributed (IID)…

Information Theory · Computer Science 2021-06-07 Lei Liu , Shunqi Huang , Brian M. Kurkoski

Approximate message passing (AMP) methods and their variants have attracted considerable recent attention for the problem of estimating a random vector $\mathbf{x}$ observed through a linear transform $\mathbf{A}$. In the case of large…

Information Theory · Computer Science 2018-03-05 Sundeep Rangan , Philip Schniter , Alyson K. Fletcher , Subrata Sarkar

The estimation of a random vector with independent components passed through a linear transform followed by a componentwise (possibly nonlinear) output map arises in a range of applications. Approximate message passing (AMP) methods, based…

Information Theory · Computer Science 2016-05-03 Sundeep Rangan , Philip Schniter , Erwin Riegler , Alyson Fletcher , Volkan Cevher

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…

Statistics Theory · Mathematics 2023-02-08 Gen Li , Wei Fan , Yuting Wei

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

We introduce Tree-AMP, standing for Tree Approximate Message Passing, a python package for compositional inference in high-dimensional tree-structured models. The package provides a unifying framework to study several approximate message…

Machine Learning · Statistics 2023-04-19 Antoine Baker , Benjamin Aubin , Florent Krzakala , Lenka Zdeborová

We consider the problem of localizing change points in a generalized linear model (GLM), a model that covers many widely studied problems in statistical learning including linear, logistic, and rectified linear regression. We propose a…

Machine Learning · Statistics 2025-09-08 Gabriel Arpino , Xiaoqi Liu , Julia Gontarek , Ramji Venkataramanan

Characterizing the distribution of high-dimensional statistical estimators is a challenging task, due to the breakdown of classical asymptotic theory in high dimension. This paper makes progress towards this by developing non-asymptotic…

Statistics Theory · Mathematics 2024-01-09 Gen Li , Yuting Wei

Given a high-dimensional data matrix ${\boldsymbol A}\in{\mathbb R}^{m\times n}$, Approximate Message Passing (AMP) algorithms construct sequences of vectors ${\boldsymbol u}^t\in{\mathbb R}^n$, ${\boldsymbol v}^t\in{\mathbb R}^m$, indexed…

Information Theory · Computer Science 2017-08-15 Raphael Berthier , Andrea Montanari , Phan-Minh Nguyen

Motivated by the recent interest in approximate message passing (AMP) for matrix-valued linear observations with superposition of \emph{multiple statistically asymmetric signal sources}, we introduce a multi-source AMP framework in which…

Information Theory · Computer Science 2025-01-22 Burak Çakmak , Giuseppe Caire

This letter proposes a novel message-passing algorithm for signal recovery in compressed sensing. The proposed algorithm solves the disadvantages of approximate message-passing (AMP) and orthogonal/vector AMP, and realizes their advantages.…

Information Theory · Computer Science 2020-04-22 Keigo Takeuchi

Approximate message passing (AMP) emerges as an effective iterative paradigm for solving high-dimensional statistical problems. However, prior AMP theory -- which focused mostly on high-dimensional asymptotics -- fell short of predicting…

Statistics Theory · Mathematics 2023-03-20 Gen Li , Yuting Wei

Mean-field characterizations of first-order iterative algorithms -- including Approximate Message Passing (AMP), stochastic and proximal gradient descent, and Langevin diffusions -- have enabled a precise understanding of learning dynamics…

Statistics Theory · Mathematics 2025-07-01 Max Lovig , Tianhao Wang , Zhou Fan

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) 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…

Information Theory · Computer Science 2015-06-10 Andre Manoel , Florent Krzakala , Eric W. Tramel , Lenka Zdeborová

Approximate message passing (AMP) is an algorithmic framework for solving linear inverse problems from noisy measurements, with exciting applications such as reconstructing images, audio, hyper spectral images, and various other signals,…

Information Theory · Computer Science 2017-02-13 Junan Zhu , Ryan Pilgrim , Dror Baron

This paper introduces a framework for approximate message passing (AMP) in dynamic settings where the data at each iteration is passed through a linear operator. This framework is motivated in part by applications in large-scale,…

Statistics Theory · Mathematics 2026-01-19 Riccardo Rossetti , Bobak Nazer , Galen Reeves