Related papers: A Lower Bound on the Bayesian MSE Based on the Opt…
We show how to compute lower bounds for the supremum Bayes error if the class-conditional distributions must satisfy moment constraints, where the supremum is with respect to the unknown class-conditional distributions. Our approach makes…
The James-Stein estimator's dominance over maximum likelihood in terms of mean square error (MSE) has been one of the most celebrated results in modern statistics, suggesting that biased estimators can systematically outperform unbiased…
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…
We analyze the problem of estimating a signal from multiple measurements on a $\mbox{group action channel}$ that linearly transforms a signal by a random group action followed by a fixed projection and additive Gaussian noise. This channel…
Bayesian estimation is a powerful theoretical paradigm for the operation of quantum sensors. However, the Bayesian method for statistical inference generally suffers from demanding calibration requirements that have so far restricted its…
Machine learning models have traditionally been developed under the assumption that the training and test distributions match exactly. However, recent success in few-shot learning and related problems are encouraging signs that these models…
In statistical classification and machine learning, classification error is an important performance measure, which is minimized by the Bayes decision rule. In practice, the unknown true distribution is usually replaced with a model…
There are two major routes to address the ubiquitous family of inverse problems appearing in signal and image processing, such as denoising or deblurring. A first route relies on Bayesian modeling, where prior probabilities are used to…
Considering the problem of risk-sensitive parameter estimation, we propose a fairly wide family of lower bounds on the exponential moments of the quadratic error, both in the Bayesian and the non--Bayesian regime. This family of bounds,…
The Cram\'er-Rao bound serves as a crucial lower limit for the mean squared error of an estimator in frequentist parameter estimation. Paradoxically, it requires highly accurate prior knowledge of the estimated parameter for constructing…
This article considers Bayesian model selection via mean-field (MF) variational approximation. Towards this goal, we study the non-asymptotic properties of MF inference under the Bayesian framework that allows latent variables and model…
ReRecent studies in machine learning are based on models in which parameters or state variables are bounded restricted. These restrictions are from prior information to ensure the validity of scientific theories or structural consistency…
When designing confirmatory Phase 3 studies, one usually evaluates one or more efficacious and safe treatment option(s) based on data from previous studies. However, several retrospective research articles reported the phenomenon of…
The sample mean is often used to aggregate different unbiased estimates of a parameter, producing a final estimate that is unbiased but possibly high-variance. This paper introduces the Bayesian median of means, an aggregation rule that…
We address the problem of signal denoising via transform-domain shrinkage based on a novel $\textit{risk}$ criterion called the minimum probability of error (MPE), which measures the probability that the estimated parameter lies outside an…
This work examines risk bounds for nonparametric distributional regression estimators. For convex-constrained distributional regression, general upper bounds are established for the continuous ranked probability score (CRPS) and the…
Minimizing the Mean Squared Error (MSE) is a key objective in machine learning and is commonly used for imputing missing values. While this approach provides accurate point estimates, it introduces systematic biases in downstream analyses.…
This paper proposes an estimation framework to assess the performance of sorting over perturbed/noisy data. In particular, the recovering accuracy is measured in terms of Minimum Mean Square Error (MMSE) between the values of the sorting…
The minimum error entropy (MEE) criterion has been verified as a powerful approach for non-Gaussian signal processing and robust machine learning. However, the implementation of MEE on robust classification is rather a vacancy in the…
A common way of characterizing minimax estimators in point estimation is by moving the problem into the Bayesian estimation domain and finding a least favorable prior distribution. The Bayesian estimator induced by a least favorable prior,…