Related papers: Parameterless Optimal Approximate Message Passing
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…
We consider sparse signal reconstruction via minimization of the smoothly clipped absolute deviation (SCAD) penalty, and develop one-step replica-symmetry-breaking (1RSB) extensions of approximate message passing (AMP), termed 1RSB-AMP.…
Purpose: For quantitative susceptibility mapping (QSM), the lack of ground-truth in clinical settings makes it challenging to determine suitable parameters for the dipole inversion. We propose a probabilistic Bayesian approach for QSM with…
In phase retrieval, the goal is to recover a complex signal from the magnitude of its linear measurements. While many well-known algorithms guarantee deterministic recovery of the unknown signal using i.i.d. random measurement matrices,…
We consider large-scale linear inverse problems in Bayesian settings. We follow a recent line of work that applies the approximate message passing (AMP) framework to multi-processor (MP) computational systems, where each processor node…
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…
This paper concerns the performance of the LASSO (also knows as basis pursuit denoising) for recovering sparse signals from undersampled, randomized, noisy measurements. We consider the recovery of the signal $x_o \in \mathbb{R}^N$ from $n$…
Approximate Message Passing (AMP) algorithms enable precise characterization of certain classes of random objects in the high-dimensional limit, and have found widespread applications in fields such as signal processing, statistics, and…
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…
Parameter-free algorithms are online learning algorithms that do not require setting learning rates. They achieve optimal regret with respect to the distance between the initial point and any competitor. Yet, parameter-free algorithms do…
Approximate message passing (AMP) methods have gained recent traction in sparse signal recovery. Additional information about the signal, or \emph{side information} (SI), is commonly available and can aid in efficient signal recovery. This…
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…
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…
The ubiquity of approximately sparse data has led a variety of com- munities to great interest in compressed sensing algorithms. Although these are very successful and well understood for linear measurements with additive noise, applying…
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)…
Approximate message passing is an iterative algorithm for compressed sensing and related applications. A solid theory about the performance and convergence of the algorithm exists for measurement matrices having iid entries of zero mean.…
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…
We present a novel compressed sensing recovery algorithm - termed Bayesian Optimal Structured Signal Approximate Message Passing (BOSSAMP) - that jointly exploits the prior distribution and the structured sparsity of a signal that shall be…
Maximum a posteriori (MAP) inference in discrete-valued Markov random fields is a fundamental problem in machine learning that involves identifying the most likely configuration of random variables given a distribution. Due to the…
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…