Related papers: A Note on Functional Averages over Gaussian Ensemb…
Some eigenvalue matrix models possess an interesting property: one can manifestly define the basis where all averages can be explicitly calculated. For example, in the Gaussian Hermitian and rectangular complex models, averages of the Schur…
The time-evolving precision matrix of a piecewise-constant Gaussian graphical model encodes the dynamic conditional dependency structure of a multivariate time-series. Traditionally, graphical models are estimated under the assumption that…
This paper focuses on the problem of separately modulating and jointly estimating two independent continuous-valued parameters sent over a Gaussian multiple-access channel (MAC) under the mean square error (MSE) criterion. To this end, we…
Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…
We propose a rectangular rotational invariant estimator to recover a real matrix from noisy matrix observations coming from an arbitrary additive rotational invariant perturbation, in the large dimension limit. Using the Bayes-optimality of…
Through refined asymptotic analysis based on the normal approximation, we study how higher-order coding performance depends on the mean power as well as on finer statistics of the input power. We introduce a multifaceted power model in…
This paper considers the quantification of the prediction performance in Gaussian process regression. The standard approach is to base the prediction error bars on the theoretical predictive variance, which is a lower bound on the mean…
In this paper we consider the classical capacity problem for Gaussian measurement channels without imposing any kind of threshold condition. We prove Gaussianity of the average state of the optimal ensemble in general and discuss the…
We calculate Gaussian averages of arbitrary exponentials of the matrix variable $X$ with the help of superintegrability, which provides explicit expressions for Schur averages. As in the simpler cases the answer is expressed in terms of…
Gravitational-wave astronomers often wish to characterize the expected parameter-estimation accuracy of future observations. The Fisher matrix provides a lower bound on the spread of the maximum-likelihood estimator across noise…
An integral over the interval $(0,\pi)$ is given for the cumulative distribution function of a sum of independent gamma random variables with different scale and shape parameters. The cumulative distribution function of a positive definite…
In this work we focus on the general relay channel. We investigate the application of estimate-and-forward (EAF) to different scenarios. Specifically, we consider assignments of the auxiliary random variables that always satisfy the…
This paper focuses on the analysis of average Gaussian error probabilities in certain fading channels, i.e. we are interested in E[Q((p {\gamma})^(1/2))] where Q(.) is the Gaussian Q-function, p is a positive real number and {\gamma} is a…
A statistical mechanical framework for analyzing random linear vector channels is presented in a large system limit. The framework is based on the assumptions that the left and right singular value bases of the rectangular channel matrix…
This paper seeks an efficient algorithm for stochastic precoding to maximize the long-term average weighted sum rates throughout a multiple-input multiple-output (MIMO) network. Unlike many existing works that assume a particular…
A distributional route to Gaussianity, associated with the concept of Conservative Mixing Transformations in ensembles of random vector-valued variables, is proposed. This route is completely different from the additive mechanism…
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…
Holographic MIMO (hMIMO) systems with a massive number of individually controlled antennas N make minimum mean square error (MMSE) channel estimation particularly challenging, due to its computational complexity that scales as $N^3$ . This…
We give a hyperpfaffian formulation of partition functions and ensemble averages for Hermitian and circular ensembles when L is an arbitrary integer and \beta=L^2 and when L is an odd integer and \beta=L^2 +1.
The goal of this paper is to show that a single robust estimator of the mean of a multivariate Gaussian distribution can enjoy five desirable properties. First, it is computationally tractable in the sense that it can be computed in a time…