相关论文: State Evolution for Approximate Message Passing wi…

We consider the problem of recovering an unknown signal ${\mathbf x}\in {\mathbb R}^n$ from general nonlinear measurements obtained through a generalized linear model (GLM), i.e., ${\mathbf y}= f\left({\mathbf A}{\mathbf x}+{\mathbf…

Gradient-descent-based algorithms and their stochastic versions have widespread applications in machine learning and statistical inference. In this work we perform an analytic study of the performances of one of them, the Langevin…

We study the compressed sensing reconstruction problem for a broad class of random, band-diagonal sensing matrices. This construction is inspired by the idea of spatial coupling in coding theory. As demonstrated heuristically and…

Generalized Linear Models (GLMs), where a random vector $\mathbf{x}$ is observed through a noisy, possibly nonlinear, function of a linear transform $\mathbf{z}=\mathbf{Ax}$ arise in a range of applications in nonlinear filtering and…

Compressed sensing, allows to acquire compressible signals with a small number of measurements. In applications, a hardware implementation often requires a calibration as the sensing process is not perfectly known. Blind calibration, that…

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…

Generalized approximate message passing (GAMP) is a computationally efficient algorithm for estimating an unknown signal $w_0\in\mathbb{R}^N$ from a random linear measurement $y= Xw_0 + \epsilon\in\mathbb{R}^M$, where…

Iterative thresholding algorithms are well-suited for high-dimensional problems in sparse recovery and compressive sensing. The performance of this class of algorithms depends heavily on the tuning of certain threshold parameters. In…

Approximate message passing (AMP) algorithms have shown great promise in sparse signal reconstruction due to their low computational requirements and fast convergence to an exact solution. Moreover, they provide a probabilistic framework…

In a recent paper, the authors proposed a new class of low-complexity iterative thresholding algorithms for reconstructing sparse signals from a small set of linear measurements \cite{DMM}. The new algorithms are broadly referred to as AMP,…

Approximate message passing (AMP) is an efficient iterative signal recovery algorithm for compressed sensing (CS). For sensing matrices with independent and identically distributed (i.i.d.) Gaussian entries, the behavior of AMP can be…

The approximate master equation (AME) provides a highly accurate description of dynamical processes on networks, yet its steady states are generally analytically intractable. In this study, we develop an analytical framework to derive the…

This paper considers probabilistic estimation of a low-rank matrix from non-linear element-wise measurements of its elements. We derive the corresponding approximate message passing (AMP) algorithm and its state evolution. Relying on…

Signal recovery from unitarily invariant measurements is investigated in this paper. A message-passing algorithm is formulated on the basis of expectation propagation (EP). A rigorous analysis is presented for the dynamics of the algorithm…

We introduce LAMP: the Linear Additive Markov Process. Transitions in LAMP may be influenced by states visited in the distant history of the process, but unlike higher-order Markov processes, LAMP retains an efficient parametrization. LAMP…

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…

As Large Language Models (LLMs) move from curated training sets into open-ended real-world environments, a fundamental limitation emerges: static training cannot keep pace with continual deployment environment change. Scaling training-time…

This paper proves the convergence of Bayes-optimal orthogonal/vector approximate message-passing (AMP) to a fixed point in the large system limit. The proof is based on Bayes-optimal long-memory (LM) message-passing (MP) that is guaranteed…

In a recent work we presented a recursive algorithm to compute the matrix elements of a generic Gaussian transformation in the photon-number basis. Its purpose was to evolve a quantum state by building the transformation matrix and…

We analyse a linear regression problem with nonconvex regularization called smoothly clipped absolute deviation (SCAD) under an overcomplete Gaussian basis for Gaussian random data. We propose an approximate message passing (AMP) algorithm…