Related papers: Fast, robust approximate message passing
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…
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.…
We propose regularized approximate message passing (RAMP), a low-complexity algorithm for discrete signal detection in overloaded multiple-input multiple-output (MIMO) systems where the number of transmit antennas exceeds the number of…
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…
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…
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,…
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…
Approximate message passing (AMP) is a low-cost iterative signal recovery algorithm for linear system models. When the system transform matrix has independent identically distributed (IID) Gaussian entries, the performance of AMP can be…
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…
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…
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…
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…
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…
We consider matrix factorization (MF) with certain constraints, which finds wide applications in various areas. Leveraging variational inference (VI) and unitary approximate message passing (UAMP), we develop a Bayesian approach to MF with…
Generalized approximate message passing (GAMP) is a promising technique for unknown signal reconstruction of generalized linear models (GLM). However, it requires that the transformation matrix has independent and identically distributed…
This paper presents a unified framework for constructing Approximate Message Passing (AMP) algorithms for rotationally-invariant models. By employing a general iterative algorithm template and reducing it to long-memory Orthogonal AMP…
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…
Message-passing (MP) is a powerful tool for finding an approximate solution in optimization. We generalize it to nonlinear product-sum form, and numerically show the fast convergence for the minimum feedback vertex set and the minimum…
We extend the generalized approximate message passing (G-AMP) approach, originally proposed for high-dimensional generalized-linear regression in the context of compressive sensing, to the generalized-bilinear case, which enables its…
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.…