Related papers: Bayesian Estimation with Distance Bounds
We address Bayesian persuasion between a sender and a receiver with state-dependent quadratic cost measures for general classes of distributions. The receiver seeks to make mean-square-error estimate of a state based on a signal sent by the…
A lower bound is an important tool for predicting the performance that an estimator can achieve under a particular statistical model. Bayesian bounds are a kind of such bounds which not only utilizes the observation statistics but also…
A difficulty in MSE estimation occurs because we do not specify a full distribution for the survey weights. This obfuscates the use of fully parametric bootstrap procedures. To overcome this challenge, we develop a novel MSE estimator. We…
A simple yet efficient method of linear regression estimation (LRE) is presented for quantum state tomography. In this method, quantum state reconstruction is converted into a parameter estimation problem of a linear regression model and…
In this paper, we investigate the statistical convergence rate of a Bayesian low-rank tensor estimator. Our problem setting is the regression problem where a tensor structure underlying the data is estimated. This problem setting occurs in…
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…
We consider distributed statistical optimization in one-shot setting, where there are $m$ machines each observing $n$ i.i.d. samples. Based on its observed samples, each machine sends a $B$-bit-long message to a server. The server then…
In this letter, we consider two sets of observations defined as subspace signals embedded in noise and we wish to analyze the distance between these two subspaces. The latter entails evaluating the angles between the subspaces, an issue…
We consider the problem of estimating the means $\mu_i$ of $n$ random variables $Y_i \sim N(\mu_i,1)$, $i=1,\ldots ,n$. Assuming some structure on the $\mu$ process, e.g., a state space model, one may use a summary statistics for the…
We consider benchmarked empirical Bayes (EB) estimators under the basic area-level model of Fay and Herriot while requiring the standard benchmarking constraint. In this paper we determine the excess mean squared error (MSE) from…
Bayesian quantum estimation provides a robust framework for quantum technologies, especially in scenarios with limited data and minimal prior information. Yet, its application to continuous-variable Gaussian systems has remained limited and…
In many instances, the application of approximate Bayesian methods is hampered by two practical features: 1) the requirement to project the data down to low-dimensional summary, including the choice of this projection, which ultimately…
We consider Bayesian inference of signals with vector-valued entries. Extending concentration techniques from the mathematical physics of spin glasses, we show that the matrix-valued minimum mean-square error concentrates when the size of…
This paper proposes a new family of lower and upper bounds on the minimum mean squared error (MMSE). The key idea is to minimize/maximize the MMSE subject to the constraint that the joint distribution of the input-output statistics lies in…
In this paper, the problem of state estimation, in the context of both filtering and smoothing, for nonlinear state-space models is considered. Due to the nonlinear nature of the models, the state estimation problem is generally intractable…
Sparse coding refers to the pursuit of the sparsest representation of a signal in a typically overcomplete dictionary. From a Bayesian perspective, sparse coding provides a Maximum a Posteriori (MAP) estimate of the unknown vector under a…
We present an algorithm for the problem of linear distributed estimation of a parameter in a network where a set of agents are successively taking measurements. The approach considers a roaming token in a network that carries the estimate,…
This paper considers the state estimation problem for discrete-time linear systems under event-triggered scheme. In order to improve performance, a novel event-triggered scheme based on confidence level is proposed using the chi-square…
The state estimation problem for nonlinear systems with stochastic uncertainties can be formulated in the Bayesian framework, where the objective is to replace the state completely by its probability density function. Without the…
We consider the Bayesian optimal filtering problem: i.e. estimating some conditional statistics of a latent time-series signal from an observation sequence. Classical approaches often rely on the use of assumed or estimated transition and…