Related papers: A leave-one-out approach to approximate message pa…
Markov chain Monte Carlo algorithms have long been observed to obtain near-optimal performance in various Bayesian inference settings. However, developing a supporting theory that makes these studies rigorous has proved challenging. In this…
Sparse regression codes with approximate message passing (AMP) decoding have gained much attention in recent times. The concepts underlying this coding scheme extend to unsourced access with coded compressed sensing (CCS), as first pointed…
Sparse Group LASSO (SGL) is a regularized model for high-dimensional linear regression problems with grouped covariates. SGL applies $l_1$ and $l_2$ penalties on the individual predictors and group predictors, respectively, to guarantee…
In many contexts, there is interest in selecting the most important variables from a very large collection, commonly referred to as support recovery or variable, feature or subset selection. There is an enormous literature proposing a rich…
Understanding efficiency in high dimensional linear models is a longstanding problem of interest. Classical work with smaller dimensional problems dating back to Huber and Bickel has illustrated the benefits of efficient loss functions.…
We show how the notion of message passing can be used to streamline the algebra and computer coding for fast approximate inference in large Bayesian semiparametric regression models. In particular, this approach is amenable to handling…
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…
This paper proposes a fast approximate message-passing (AMP) algorithm for solving compressed sensing (CS) recovery problems with 1D-finite-difference sparsity in term of MMSE estimation. The proposed algorithm, named ssAMP-BGFD, is…
We discuss the prediction accuracy of assumed statistical models in terms of prediction errors for the generalized linear model and penalized maximum likelihood methods. We derive the forms of estimators for the prediction errors, such as…
Improved mean-field technics are a central theme of statistical physics methods applied to inference and learning. We revisit here some of these methods using high-temperature expansions for disordered systems initiated by Plefka, Georges…
Approximate Message Passing (AMP), originally developed to address high-dimensional linear inverse problems, has found widespread applications in signal processing and statistical inference. Among its notable variants, Vector Approximate…
In this paper, we study a spiked Wigner problem with an inhomogeneous noise profile. Our aim in this problem is to recover the signal passed through an inhomogeneous low-rank matrix channel. While the information-theoretic performances are…
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…
The future predictive performance of a Bayesian model can be estimated using Bayesian cross-validation. In this article, we consider Gaussian latent variable models where the integration over the latent values is approximated using the…
We study asymptotic properties of expectation propagation (EP) -- a method for approximate inference originally developed in the field of machine learning. Applied to generalized linear models, EP iteratively computes a multivariate…
Recovering a sparse signal from an undersampled set of random linear measurements is the main problem of interest in compressed sensing. In this paper, we consider the case where both the signal and the measurements are complex. We study…
With a unified belief propagation (BP) and mean field (MF) framework, we propose an iterative message passing receiver, which performs joint channel state and noise precision (the reciprocal of noise variance) estimation and decoding for…
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.…
Vector Approximate Message Passing (VAMP) provides the means of solving a linear inverse problem in a Bayes-optimal way assuming the measurement operator is sufficiently random. However, VAMP requires implementing the linear minimum mean…
We study the problem of estimating a rank one signal matrix from an observed matrix generated by corrupting the signal with additive rotationally invariant noise. We develop a new class of approximate message-passing algorithms for this…