May 5, 2021 · Abstract: Over the last decade or so, Approximate Message Passing (AMP) algorithms have become extremely popular in various structured high-dimensional statistical problems. The fact that the origins of these techniques can be traced back to notions of belief propagation in the statistical physics literature lends a certain mystique to the area ...

Jan 19, 2022 · The approximate message passing (AMP) algorithm proposed by Donoho \textit{et al} is a computational efficient method to such problems, which can attain Bayes-optimal performance in independent identical distributed (IID) sub-Gaussian random matrices region.

The approximate message passing (AMP) algorithm is used to calculate x^ = h˙i . 2 ISTA and FISTA for LASSO The convex optimization problem de ning LASSO has structure x^ LASSO= argmin x 1 2n ky Axk2 2 | {z } convex di erentiable f(x) + n kxk 1 |{z} convex separable g(x): 1

Nov 5, 2024 · 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...

We study them both theoretically and empirically. We will also introduce a new class of algorithms called approximate message passing or AMP. These schemes have several advantages over the classical thresholding approaches.

A Unifying Tutorial on Approximate Message Passing Abstract: Over the last decade, Approximate Message Passing (AMP) algorithms have become extremely popular in various structured high-dimensional statistical problems.

Aug 26, 2021 · Approximate Message Passing (AMP) refers to a class of iterative algorithms that have been successfully applied to a number of high-dimensional statistical estimation problems like linear regression, generalized linear models, and low-rank matrix estimation, and a variety of engineering and computer science applications such as imaging ...

Approximate Message Passing algorithms are a versatile family of iterative algorithms that have found applications in various statistical problems. This thesis highlights some of the recent advancements that generalize the applicability of AMP. First, we analyze the universality of AMP algorithms, showing that their state evolutions hold over a broader range of random matrices, including those ...

Approximate Message Passing Mohsen Bayati, David Donoho, Adel Jaanmardv Iain Johnstone, Marc Lelarge, Arian Maleki, Andrea Montanari Stanford University December 8, 2012 Andrea Montanari (Stanford) AMP December 8, 2012 1 / 68. Statistical estimation y = f ( ; noise ) ! Unknown object y ! Observations

A Python implementation of Approximate Message Passing (AMP) algorithms for LASSO Resources