English
Related papers

Related papers: Estimation in Rotationally Invariant Generalized L…

200 papers

Gaussian and quadratic approximations of message passing algorithms on graphs have attracted considerable recent attention due to their computational simplicity, analytic tractability, and wide applicability in optimization and statistical…

Information Theory · Computer Science 2026-03-12 Sundeep Rangan , Alyson K. Fletcher , Vivek K. Goyal , Evan Byrne , Philip Schniter

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

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

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

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

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

Approximate Message Passing (AMP) algorithms have seen widespread use across a variety of applications. However, the precise forms for their Onsager corrections and state evolutions depend on properties of the underlying random matrix…

Probability · Mathematics 2021-08-16 Zhou Fan

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) 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) algorithms have become an important element of high-dimensional statistical inference, mostly due to their adaptability and concentration properties, the state evolution (SE) equations. This is demonstrated…

Information Theory · Computer Science 2022-04-20 Cédric Gerbelot , Raphaël Berthier

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

Vector approximate message passing (VAMP) is an efficient approximate inference algorithm used for generalized linear models. Although VAMP exhibits excellent performance, particularly when measurement matrices are sampled from rotationally…

Information Theory · Computer Science 2025-08-05 Takashi Takahashi , Yoshiyuki Kabashima

We consider the problem of reconstructing a signal from multi-layered (possibly) non-linear measurements. Using non-rigorous but standard methods from statistical physics we present the Multi-Layer Approximate Message Passing (ML-AMP)…

Information Theory · Computer Science 2020-01-22 Andre Manoel , Florent Krzakala , Marc Mézard , 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

Recently we extended Approximate message passing (AMP) algorithm to be able to handle general invariant matrix ensembles. In this contribution we extend our S-AMP approach to non-linear observation models. We obtain generalized AMP (GAMP)…

Information Theory · Computer Science 2015-01-27 Burak Çakmak , Ole Winther , Bernard H. Fleury

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…

Probability · Mathematics 2023-05-02 Rishabh Dudeja , Yue M. Lu , Subhabrata Sen

The standard linear regression (SLR) problem is to recover a vector $\mathbf{x}^0$ from noisy linear observations $\mathbf{y}=\mathbf{Ax}^0+\mathbf{w}$. The approximate message passing (AMP) algorithm recently proposed by Donoho, Maleki,…

Information Theory · Computer Science 2018-07-24 Sundeep Rangan , Philip Schniter , Alyson K. Fletcher

Designing efficient sparse recovery algorithms that could handle noisy quantized measurements is important in a variety of applications -- from radar to source localization, spectrum sensing and wireless networking. We take advantage of the…

Signal Processing · Electrical Eng. & Systems 2022-05-24 Shuai Huang , Deqiang Qiu , Trac D. Tran

In this paper, we address the problem of recovering complex-valued signals from a set of complex-valued linear measurements. Approximate message passing (AMP) is one state-of-the-art algorithm to recover real-valued sparse signals. However,…

Information Theory · Computer Science 2016-01-26 Xiangming Meng , Sheng Wu , Linling Kuang , Jianhua Lu

Approximate Message Passing (AMP) is an efficient iterative parameter-estimation technique for certain high-dimensional linear systems with non-Gaussian distributions, such as sparse systems. In AMP, a so-called Onsager term is added to…

Information Theory · Computer Science 2023-01-16 Lei Liu , Yiyao Cheng , Shansuo Liang , Jonathan H. Manton , Li Ping