Related papers: A Lower Bound on the Bayesian MSE Based on the Opt…

In parametric Bayesian learning, a prior is assumed on the parameter $W$ which determines the distribution of samples. In this setting, Minimum Excess Risk (MER) is defined as the difference between the minimum expected loss achievable when…

Consider the minimum mean-square error (MMSE) of estimating an arbitrary random variable from its observation contaminated by Gaussian noise. The MMSE can be regarded as a function of the signal-to-noise ratio (SNR) as well as a functional…

Bias reduction in tail estimation has received considerable interest in extreme value analysis. Estimation methods that minimize the bias while keeping the mean squared error (MSE) under control, are especially useful when applying…

Purpose: To develop neural network (NN)-based quantitative MRI parameter estimators with minimal bias and a variance close to the Cram\'er-Rao bound. Theory and Methods: We generalize the mean squared error loss to control the bias and…

In this paper, we address the theoretical limitations in reconstructing sparse signals (in a known complete basis) using compressed sensing framework. We also divide the CS to non-blind and blind cases. Then, we compute the Bayesian…

Bayesian neural networks perform variational inference over the weights however calculation of the posterior distribution remains a challenge. Our work builds on variational inference techniques for bayesian neural networks using the…

In this paper, we propose a sparse signal estimation algorithm that is suitable for many wireless communication systems, especially for the future millimeter wave and underwater communication systems. This algorithm is not only…

We present a new method to propagate lower bounds on conditional probability distributions in conventional Bayesian networks. Our method guarantees to provide outer approximations of the exact lower bounds. A key advantage is that we can…

We address the problem of estimating the transmissivity of the pure-loss channel from the Bayesian point of view, i.e., we consider that some prior probability distribution function (PDF) on the unknown variable is available and we employ…

State estimation is a classical problem in quantum information. In optimization of estimation scheme, to find a lower bound to the error of the estimator is a very important step. So far, all the proposed tractable lower bounds use…

The problem of astrometry is revisited from the perspective of analyzing the attainability of well-known performance limits (the Cramer-Rao bound) for the estimation of the relative position of light-emitting (usually point-like) sources on…

Characterizing the performance trade-offs between sensing and communication subsystems is essential for enabling integrated sensing and communication systems. Various metrics exist for each subsystem; however, this study focuses on the…

Tight bounds on the minimum mean square error for the additive Gaussian noise channel are derived, when the input distribution is constrained to be epsilon-close to a Gaussian reference distribution in terms of the Kullback--Leibler…

Bagging can significantly improve the generalization performance of unstable machine learning algorithms such as trees or neural networks. Though bagging is now widely used in practice and many empirical studies have explored its behavior,…

We derive lower bounds on the Bayes risk in decentralized estimation, where the estimator does not have direct access to the random samples generated conditionally on the random parameter of interest, but only to the data received from…

Squared error loss remains the most commonly used loss function for constructing a Bayes estimator of the parameter of interest. However, it can lead to sub-optimal solutions when a parameter is defined in a restricted space. It can also be…

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…

The constrained Cramer-Rao bound (CCRB) is a lower bound on the mean-squared-error (MSE) of estimators that satisfy some unbiasedness conditions. Although the CCRB unbiasedness conditions are satisfied asymptotically by the constrained…

In a unified viewpoint in quantum channel estimation, we compare the Cramer-Rao and the mini-max approaches, which gives the Bayesian bound in the group covariant model. For this purpose, we introduce the local asymptotic mini-max bound,…

In data-driven learning and inference tasks, the high cost of acquiring samples from the target distribution often limits performance. A common strategy to mitigate this challenge is to augment the limited target samples with data from a…