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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

Optimizing a high-dimensional non-convex function is, in general, computationally hard and many problems of this type are hard to solve even approximately. Complexity theory characterizes the optimal approximation ratios achievable in…

Statistical Mechanics · Physics 2020-09-25 Ahmed El Alaoui , Andrea Montanari

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

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

A common goal in many research areas is to reconstruct an unknown signal x from noisy linear measurements. Approximate message passing (AMP) is a class of low-complexity algorithms for efficiently solving such high-dimensional regression…

Information Theory · Computer Science 2019-05-07 Hangjin Liu , Cynthia Rush , Dror Baron

We consider a class of nonlinear mappings $\mathsf{F}_{A,N}$ in $\mathbb{R}^N$ indexed by symmetric random matrices $A\in\mathbb{R}^{N\times N}$ with independent entries. Within spin glass theory, special cases of these mappings correspond…

Probability · Mathematics 2015-03-18 Mohsen Bayati , Marc Lelarge , Andrea Montanari

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) is a class of efficient algorithms for solving high-dimensional linear regression tasks where one wishes to recover an unknown signal \beta_0 from noisy, linear measurements y = A \beta_0 + w. When applying…

Information Theory · Computer Science 2017-08-15 Yanting Ma , Cynthia Rush , Dror Baron

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

Solving a large-scale regularized linear inverse problem using multiple processors is important in various real-world applications due to the limitations of individual processors and constraints on data sharing policies. This paper focuses…

Information Theory · Computer Science 2017-01-31 Yanting Ma , Yue M. Lu , Dror Baron

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

Generalised approximate message passing (GAMP) is an approximate Bayesian estimation algorithm for signals observed through a linear transform with a possibly non-linear subsequent measurement model. By leveraging prior information about…

Signal Processing · Electrical Eng. & Systems 2018-12-05 Christian Schou Oxvig , Thomas Arildsen

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

Information Theory · Computer Science 2022-06-24 Lei Liu , Shunqi Huang , Brian M. Kurkoski

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 estimation of an i.i.d. (possibly non-Gaussian) vector $\xbf \in \R^n$ from measurements $\ybf \in \R^m$ obtained by a general cascade model consisting of a known linear transform followed by a probabilistic componentwise…

Information Theory · Computer Science 2012-12-04 Ulugbek S. Kamilov , Sundeep Rangan , Alyson K. Fletcher , Michael Unser

A common goal in many research areas is to reconstruct an unknown signal x from noisy linear measurements. Approximate message passing (AMP) is a class of low-complexity algorithms that can be used for efficiently solving such…

Signal Processing · Electrical Eng. & Systems 2020-03-27 Hangjin Liu , Cynthia Rush , Dror Baron

The generalized approximate message passing (GAMP) algorithm is an efficient method of MAP or approximate-MMSE estimation of $x$ observed from a noisy version of the transform coefficients $z = Ax$. In fact, for large zero-mean i.i.d…

Information Theory · Computer Science 2015-08-11 Jeremy Vila , Philip Schniter , Sundeep Rangan , Florent Krzakala , Lenka Zdeborova

We study compressed sensing (CS) signal reconstruction problems where an input signal is measured via matrix multiplication under additive white Gaussian noise. Our signals are assumed to be stationary and ergodic, but the input statistics…

Information Theory · Computer Science 2016-11-03 Yanting Ma , Junan Zhu , Dror Baron

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

In this work we propose a novel iterative estimation algorithm for linear observation systems called S-AMP whose fixed points are the stationary points of the exact Gibbs free energy under a set of (first- and second-) moment consistency…

Information Theory · Computer Science 2014-05-13 Burak Çakmak , Ole Winther , Bernard H. Fleury