Related papers: The Linear Model under Mixed Gaussian Inputs: Desi…
Recently, machine learning-based channel estimation has attracted much attention. The performance of machine learning-based estimation has been validated by simulation experiments. However, little attention has been paid to the theoretical…
This note examines the behavior of generalization capabilities - as defined by out-of-sample mean squared error (MSE) - of Linear Gaussian (with a fixed design matrix) and Linear Least Squares regression. Particularly, we consider a…
We investigate whether uncoded schemes are optimal for Gaussian sources on multiuser Gaussian channels. Particularly, we consider two problems: the first is to send correlated Gaussian sources on a Gaussian broadcast channel where each…
We consider the estimation of an n-dimensional vector s from the noisy element-wise measurements of $\mathbf{s}\mathbf{s}^T$, a generic problem that arises in statistics and machine learning. We study a mismatched Bayesian inference…
This paper estimates free energy, average mutual information, and minimum mean square error (MMSE) of a linear model under two assumptions: (1) the source is generated by a Markov chain, (2) the source is generated via a hidden Markov…
We investigate the theoretical foundations of a recently introduced entropy-based formulation of weighted least squares for the approximation of overdetermined linear systems, motivated by robust data fitting in the presence of sparse gross…
Minimum mean squared error (MMSE) estimators of signals from samples corrupted by jitter (timing noise) and additive noise are nonlinear, even when the signal prior and additive noise have normal distributions. This paper develops a…
Accurate knowledge of transmission line parameters is essential for a variety of power system monitoring, protection, and control applications. The use of phasor measurement unit (PMU) data for transmission line parameter estimation (TLPE)…
We establish exact asymptotic expressions for the normalized mutual information and minimum mean-square-error (MMSE) of sparse linear regression in the sub-linear sparsity regime. Our result is achieved by a generalization of the adaptive…
In this paper, we investigate Gaussian process regression models where inputs are subject to measurement error. In spatial statistics, input measurement errors occur when the geographical locations of observed data are not known exactly.…
The linear minimum mean squared error (LMMSE) estimator is the best linear estimator for a Bayesian linear inverse problem with respect to the mean squared error. It arises as the solution operator to a Tikhonov-type regularized inverse…
This paper gives a replica analysis for the minimum mean square error (MSE) of a massive multiple-input multiple-output (MIMO) system by using Bayesian inference. The Bayes-optimal estimator is adopted to estimate the data symbols and the…
The problem of estimating an arbitrary random vector from its observation corrupted by additive white Gaussian noise, where the cost function is taken to be the Minimum Mean $p$-th Error (MMPE), is considered. The classical Minimum Mean…
We consider the problem of sequentially learning to estimate, in the mean squared error (MSE) sense, a Gaussian $K$-vector of unknown covariance by observing only $m < K$ of its entries in each round. We propose two MSE estimators, and…
We propose an adversarial evaluation framework for sensitive feature inference based on minimum mean-squared error (MMSE) estimation with a finite sample size and linear predictive models. Our approach establishes theoretical lower bounds…
Accurate channel estimation is critical for realizing the performance gains of massive multiple-input multiple-output (MIMO) systems. Traditional approaches to channel estimation typically assume ideal receiver hardware and linear signal…
Linear minimum mean square error (LMMSE) estimation is often ill-conditioned, suggesting that unconstrained minimization of the mean square error is an inadequate approach to filter design. To address this, we first develop a unifying…
Consider the problem of estimating the mean of a Gaussian random vector when the mean vector is assumed to be in a given convex set. The most natural solution is to take the Euclidean projection of the data vector on to this convex set; in…
We introduce a new analysis of an adaptive mixture method that combines outputs of two constituent filters running in parallel to model an unknown desired signal. This adaptive mixture is shown to achieve the mean square error (MSE)…
In this paper, we study a generalized Kalman-Bucy filtering problem under uncertainty. The drift uncertainty for both signal process and observation process is considered and the attitude to uncertainty is characterized by a convex operator…