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Approximate message passing (AMP) type algorithms have been widely used in the signal reconstruction of certain large random linear systems. A key feature of the AMP-type algorithms is that their dynamics can be correctly described by state…

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

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 propose an orthogonal approximate message passing (OAMP) algorithm for signal estimation in the rectangular spiked matrix model with general rotationally invariant (RI) noise. We establish a rigorous state evolution that exactly…

Statistics Theory · Mathematics 2026-02-04 Haohua Chen , Songbin Liu , Junjie Ma

Support vector machines (SVMs) with sparsity-inducing nonconvex penalties have received considerable attentions for the characteristics of automatic classification and variable selection. However, it is quite challenging to solve the…

Machine Learning · Statistics 2018-09-12 Lei Guan , Linbo Qiao , Dongsheng Li , Tao Sun , Keshi Ge , Xicheng Lu

Recently, Approximate Message Passing (AMP) has been integrated with stochastic localization (diffusion model) by providing a computationally efficient estimator of the posterior mean. Existing (rigorous) analysis typically proves the…

Statistics Theory · Mathematics 2025-03-18 Han Cui , Zhiyuan Yu , Jingbo Liu

X-ray Computed Tomography (CT) reconstruction from a sparse number of views is a useful way to reduce either the radiation dose or the acquisition time, for example in fixed-gantry CT systems, however this results in an ill-posed inverse…

Data Structures and Algorithms · Computer Science 2020-11-04 Alessandro Perelli , Michael Lexa , Ali Can , Mike E. Davies

We introduce an iterative optimization scheme for convex objectives consisting of a linear loss and a non-separable penalty, based on the expectation-consistent approximation and the vector approximate message-passing (VAMP) algorithm.…

Machine Learning · Statistics 2018-09-18 Andre Manoel , Florent Krzakala , Gaël Varoquaux , Bertrand Thirion , Lenka Zdeborová

In many real-world problems, recovering sparse signals from underdetermined linear systems remains a fundamental challenge. Although $\ell_1$ norm minimization is widely used, it suffers from estimation bias that prevents it from reaching…

Information Theory · Computer Science 2026-04-16 Keisuke Morita , Federico Ricci-Tersenghi , Masayuki Ohzeki

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…

Information Theory · Computer Science 2022-03-02 Qiuyun Zou , Hongwen Yang

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

Approximate Message Passing (AMP) is a general framework for iterative algorithms, originally developed for compressed sensing and later extended to a wide range of high-dimensional inference problems. Although recent work has advanced…

Signal Processing · Electrical Eng. & Systems 2026-04-24 Vishnu Teja Kunde , Alessandro Mirri , Jean-Francois Chamberland , Enrico Paolini

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…

Information Theory · Computer Science 2017-06-20 Alyson K. Fletcher , Mojtaba Sahraee-Ardakan , Philip Schniter , Sundeep Rangan

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

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

Approximate Message Passing (AMP) algorithms are a class of iterative procedures for computationally-efficient estimation in high-dimensional inference and estimation tasks. Due to the presence of an 'Onsager' correction term in its…

Statistics Theory · Mathematics 2023-02-02 Collin Cademartori , Cynthia Rush

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…

Data Structures and Algorithms · Computer Science 2023-11-16 Misha Ivkov , Tselil Schramm

We consider the problem of signal estimation in generalized linear models defined via rotationally invariant design matrices. Since these matrices can have an arbitrary spectral distribution, this model is well suited for capturing complex…

Machine Learning · Statistics 2022-06-10 Ramji Venkataramanan , Kevin Kögler , Marco Mondelli

Recovering a sparse signal from an undersampled set of random linear measurements is the main problem of interest in compressed sensing. In this paper, we consider the case where both the signal and the measurements are complex. We study…

Information Theory · Computer Science 2015-03-19 Arian Maleki , Laura Anitori , Zai Yang , Richard Baraniuk

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 (AMP) type algorithms have been widely used in the signal reconstruction of certain large random linear systems. A key feature of the AMP-type algorithms is that their dynamics can be correctly described by state…

Information Theory · Computer Science 2023-07-03 Lei Liu , Shunqi Huang , YuZhi Yang , Zhaoyang Zhang , Brian M. Kurkoski