Related papers: Cramer Rao-Type Bounds for Sparse Bayesian Learnin…

The posterior Cram\'er-Rao lower bound (PCRLB) derived in Tichavsk\'y et al., 1998, provides a bound on the mean square error (MSE) obtained with any non-linear state filter. Computing the PCRLB involves solving complex, multi-dimensional…

This study addresses the problem of discrete signal reconstruction from the perspective of sparse Bayesian learning (SBL). Generally, it is intractable to perform the Bayesian inference with the ideal discretization prior under the SBL…

In this paper, the Cramer Rao bound (CRB) for range estimation between two underwater nodes is calculated under a Gaussian noise assumption on the measurements. The nodes can measure their depths, their mutual time of flight, and they have…

We extend the traditional framework for estimating subspace bases that maximize the preserved signal energy to additionally preserve the Cram\'er-Rao bound (CRB) of the biophysical parameters and, ultimately, improve accuracy and precision…

The linear regression model with a random variable (RV) measurement matrix, where the mean of the random measurement matrix has full column rank, has been extensively studied. In particular, the quasiconvexity of the maximum likelihood…

Building on the framework introduced by Xu and Raginksy [1] for supervised learning problems, we study the best achievable performance for model-based Bayesian reinforcement learning problems. With this purpose, we define minimum Bayesian…

In this paper, tight upper and lower bounds are derived on the weighted sum of minimum mean-squared errors for additive Gaussian noise channels. The bounds are obtained by constraining the input distribution to be close to a Gaussian…

We consider minimum variance estimation within the sparse linear Gaussian model (SLGM). A sparse vector is to be estimated from a linearly transformed version embedded in Gaussian noise. Our analysis is based on the theory of reproducing…

In this paper, a sparse signal recovery algorithm using Bayesian linear regression with Cauchy prior (BLRC) is proposed. Utilizing an approximate expectation maximization(AEM) scheme, a systematic hyper-parameter updating strategy is…

We consider the classical problem of missing-mass estimation, which deals with estimating the total probability of unseen elements in a sample. The missing-mass estimation problem has various applications in machine learning, statistics,…

Inverse problems involving partial differential equations (PDEs) are widely used in science and engineering. Although such problems are generally ill-posed, different regularisation approaches have been developed to ameliorate this problem.…

In this paper, we consider a multiple-input multiple-output (MIMO) radar system for localizing a target based on its reflected echo signals. Specifically, we aim to estimate the random and unknown angle information of the target, by…

Sparse linear arrays, such as co-prime arrays and nested arrays, have the attractive capability of providing enhanced degrees of freedom. By exploiting the coarray structure, an augmented sample covariance matrix can be constructed and…

This paper derives a Ziv-Zakai Bound (ZZB) on the Mean Squared Error (MSE) for Direction-of-Arrival (DoA) estimation in co-located Multiple-Input Multiple-Output (MIMO) radar systems and provides closed-form expressions that hold for…

Bayesian reinforcement learning (BRL) is a method that merges principles from Bayesian statistics and reinforcement learning to make optimal decisions in uncertain environments. As a model-based RL method, it has two key components: (1)…

The conditional posterior Cramer-Rao lower bound (PCRLB) is an effective sensor resource management criteria for large, geographically distributed sensor networks. Existing algorithms for distributed computation of the PCRLB (dPCRLB) are…

The spectrum environment map (SEM), which can visualize the information of invisible electromagnetic spectrum, is vital for monitoring, management, and security of spectrum resources in cognitive radio (CR) networks. In view of a limited…

Score based learning (SBL) is a promising approach for learning Bayesian networks in the discrete domain. However, when employing SBL in the continuous domain, one is either forced to move the problem to the discrete domain or use metrics…

This paper considers mean square error (MSE) analysis for stochastic gradient sampling algorithms applied to underdamped Langevin dynamics under a global convexity assumption. A novel discrete Poisson equation framework is developed to…

This paper presents a novel variational inference framework for deriving a family of Bayesian sparse Gaussian process regression (SGPR) models whose approximations are variationally optimal with respect to the full-rank GPR model enriched…