Related papers: Generalized Approximate Message Passing for Estima…
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…
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…
Estimation of a vector from quantized linear measurements is a common problem for which simple linear techniques are suboptimal -- sometimes greatly so. This paper develops generalized approximate message passing (GAMP) algorithms for…
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…
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…
The generalized linear model (GLM), where a random vector $\boldsymbol{x}$ is observed through a noisy, possibly nonlinear, function of a linear transform output $\boldsymbol{z}=\boldsymbol{Ax}$, arises in a range of applications such as…
The generalized approximate message passing (GAMP) algorithm is an efficient method of MAP or approximate-MMSE estimation of $x$ observed from a noisy version of the transform coefficients $z = Ax$. In fact, for large zero-mean i.i.d…
We consider the problem of signal estimation in generalized linear models defined via rotationally invariant design matrices. Since these matrices can have an arbitrary spectral distribution, this model is well suited for capturing complex…
Approximate Message Passing (AMP) algorithms are a class of iterative procedures for computationally-efficient estimation in high-dimensional inference and estimation tasks. Due to the presence of an 'Onsager' correction term in its…
Approximate message passing (AMP) methods and their variants have attracted considerable recent attention for the problem of estimating a random vector $\mathbf{x}$ observed through a linear transform $\mathbf{A}$. In the case of large…
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…
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…
In Generalized Linear Estimation (GLE) problems, we seek to estimate a signal that is observed through a linear transform followed by a component-wise, possibly nonlinear and noisy, channel. In the Bayesian optimal setting, Generalized…
We consider the problem of reconstructing the signal and the hidden variables from observations coming from a multi-layer network with rotationally invariant weight matrices. The multi-layer structure models inference from deep generative…
Approximate message passing (AMP) algorithms are devised under the Gaussianity assumption of the measurement noise vector. In this work, we relax this assumption within the vector AMP (VAMP) framework to arbitrary independent and…
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…
Generalized Vector Approximate Message Passing (GVAMP) is an efficient iterative algorithm for approximately minimum-mean-squared-error estimation of a random vector $\mathbf{x}\sim p_{\mathbf{x}}(\mathbf{x})$ from generalized linear…
The sparse Beyesian learning (also referred to as Bayesian compressed sensing) algorithm is one of the most popular approaches for sparse signal recovery, and has demonstrated superior performance in a series of experiments. Nevertheless,…
For the problem of binary linear classification and feature selection, we propose algorithmic approaches to classifier design based on the generalized approximate message passing (GAMP) algorithm, recently proposed in the context of…
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…