Related papers: A unifying tutorial on Approximate Message Passing
Mean-field characterizations of first-order iterative algorithms -- including Approximate Message Passing (AMP), stochastic and proximal gradient descent, and Langevin diffusions -- have enabled a precise understanding of learning dynamics…
Approximate message passing (AMP) is a class of efficient algorithms for solving high-dimensional linear regression tasks where one wishes to recover an unknown signal \beta_0 from noisy, linear measurements y = A \beta_0 + w. When applying…
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…
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…
In this paper, we address the problem of recovering complex-valued signals from a set of complex-valued linear measurements. Approximate message passing (AMP) is one state-of-the-art algorithm to recover real-valued sparse signals. However,…
A concise expectation propagation (EP) based message passing algorithm (MPA) is derived for the general measurement channel. By neglecting some high-order infinitesimal terms, the EP-MPA is proven to be equivalent to the Generalized…
In the pooled data problem, the goal is to identify the categories associated with a large collection of items via a sequence of pooled tests. Each pooled test reveals the number of items of each category within the pool. We study an…
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…
Recently, several promising approximate message passing (AMP) based algorithms have been developed for bilinear recovery with model $\boldsymbol{Y}=\sum_{k=1}^K b_k \boldsymbol{A}_k \boldsymbol{C} +\boldsymbol{W} $, where $\{b_k\}$ and…
1-bit compressive sensing aims to recover sparse signals from quantized 1-bit measurements. Designing efficient approaches that could handle noisy 1-bit measurements is important in a variety of applications. In this paper we use the…
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…
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…
This paper presents a unified framework to understand the dynamics of message-passing algorithms in compressed sensing. State evolution is rigorously analyzed for a general error model that contains the error model of approximate…
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…
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…
Embeddings are a basic initial feature extraction step in many machine learning models, particularly in natural language processing. An embedding attempts to map data tokens to a low-dimensional space where similar tokens are mapped to…
We study a class of Approximate Message Passing (AMP) algorithms for symmetric and rectangular spiked random matrix models with orthogonally invariant noise. The AMP iterates have fixed dimension $K \geq 1$, a multivariate non-linearity is…
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)…
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…
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…