Related papers: Estimation for High-Dimensional Multi-Layer Genera…
This is Part II of a two-part work on the estimation for a multi-layer generalized linear model (ML-GLM) in large system limits. In Part I, we had analyzed the asymptotic performance of an exact MMSE estimator, and obtained a set of coupled…
We consider the problem of signal estimation in a generalized linear model (GLM). GLMs include many canonical problems in statistical estimation, such as linear regression, phase retrieval, and 1-bit compressed sensing. Recent work has…
In this paper, we consider the problem of recovering random graph signals with complex values. For general Bayesian estimation of complex-valued vectors, it is known that the widely-linear minimum mean-squared-error (WLMMSE) estimator can…
We study the excess mean square error (EMSE) above the minimum mean square error (MMSE) in large linear systems where the posterior mean estimator (PME) is evaluated with a postulated prior that differs from the true prior of the input…
Deep generative networks provide a powerful tool for modeling complex data in a wide range of applications. In inverse problems that use these networks as generative priors on data, one must often perform inference of the inputs of the…
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)…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
Deep generative priors offer powerful models for complex-structured data, such as images, audio, and text. Using these priors in inverse problems typically requires estimating the input and/or hidden signals in a multi-layer deep neural…
When recovering an unknown signal from noisy measurements, the computational difficulty of performing optimal Bayesian MMSE (minimum mean squared error) inference often necessitates the use of maximum a posteriori (MAP) inference, a special…
Deep generative priors are a powerful tool for reconstruction problems with complex data such as images and text. Inverse problems using such models require solving an inference problem of estimating the input and hidden units of the…
Millimeter-wave massive multiple-input multiple-output (MIMO) can use a lens antenna array to considerably reduce the number of radio frequency (RF) chains, but channel estimation is challenging due to the number of RF chains is much…
Sparse inverse covariance estimation (i.e., edge de-tection) is an important research problem in recent years, wherethe goal is to discover the direct connections between a set ofnodes in a networked system based upon the observed…
The recent work `A unified Bayesian inference framework for generalized linear models' \cite{meng1} shows that the GLM can be solved via iterating between the standard linear module (SLM) (running with standard Bayesian algorithm) and the…
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…
We consider distributed estimation of a Gaussian source in a heterogenous bandwidth constrained sensor network, where the source is corrupted by independent multiplicative and additive observation noises, with incomplete statistical…
Learning a Gaussian Mixture Model (GMM) is hard when the number of parameters is too large given the amount of available data. As a remedy, we propose restricting the GMM to a Gaussian Markov Random Field Mixture Model (GMRF-MM), as well as…
Generalized linear models (GLMs) arise in high-dimensional machine learning, statistics, communications and signal processing. In this paper we analyze GLMs when the data matrix is random, as relevant in problems such as compressed sensing,…
High-dimensional datasets are frequently subject to contamination by outliers and heavy-tailed noise, which can severely bias standard regularized estimators like the Lasso. While Maximum Mean Discrepancy (MMD) has recently been introduced…
Machine learning (ML) starts to be widely used to enhance the performance of multi-user multiple-input multiple-output (MU-MIMO) receivers. However, it is still unclear if such methods are truly competitive with respect to conventional…
To glean the benefits offered by massive multi-input multi-output (MIMO) systems, channel state information must be accurately acquired. Despite the high accuracy, the computational complexity of classical linear minimum mean squared error…