Related papers: Inequalities for the Bayes Risk
We present a general approach, based on exponential inequalities, to derive bounds on the generalization error of randomized learning algorithms. Using this approach, we provide bounds on the average generalization error as well as bounds…
New results related to the Boas-Bellman generalisation of Bessel's inequality in inner product spaces are given.
We obtain some new inequalities of Chebyshev Type.
In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware that both are fictional candidates. To study such cases,…
We study admissibility of a subclass of generalized Bayes estimators of a multivariate normal vector when the variance is unknown, under scaled quadratic loss. Minimaxity is also established for certain of these estimators.
The article addresses a long-standing open problem on the justification of using variational Bayes methods for parameter estimation. We provide general conditions for obtaining optimal risk bounds for point estimates acquired from…
Errors quoted on results are often given in asymmetric form. An account is given of the two ways these can arise in an analysis, and the combination of asymmetric errors is discussed. It is shown that the usual method has no basis and is…
The Sliced-Wasserstein distance (SW) is a computationally efficient and theoretically grounded alternative to the Wasserstein distance. Yet, the literature on its statistical properties -- or, more accurately, its generalization properties…
This paper focuses on Bayesian shrinkage for covariance matrix estimation. We examine posterior properties and frequentist risks of Bayesian estimators based on new hierarchical inverse-Wishart priors. More precisely, we give the existence…
Several inequalities of Ostrowski-Gruss-type availabe in the literature are generalized by considering the weighted case of them. Involving the least concave majorant of the modulus of continuity we provide upper error bounds of such…
We obtain variational inequalities for some classes of bilinear averages of one variable, generalizing the variational inequalities for averages of R. Jones {\it et al}. As an application we get almost everywhere convergence for the ergodic…
The Wasserstein distance quantifies the distance between two probability measures on a metric space. We prove an analogue of the Berry-Esseen inequality for the Wasserstein distance on a finite area hyperbolic surface. This inequality…
In order to give a unified generalization of the BW inequality and the DDVV inequality, Lu and Wenzel proposed three Conjectures 1, 2, 3 and an open Question 1 in 2016. In this paper we discuss further these conjectures and put forward…
In certain applications involving the solution of a Bayesian inverse problem, it may not be possible or desirable to evaluate the full posterior, e.g. due to the high computational cost of doing so. This problem motivates the use of…
Bayesian and frequentist criteria fundamentally differ, but often posterior and sampling distributions agree asymptotically (e.g., Gaussian with same covariance). For the corresponding single-draw experiment, we characterize the frequentist…
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…
Univariate and multivariate general linear regression models, subject to linear inequality constraints, arise in many scientific applications. The linear inequality restrictions on model parameters are often available from phenomenological…
This note presents families of inequalities for the Gaussian measure of convex sets which extend the recently proven Gaussian correlation inequality in various directions.
The radiological characterization of contaminated elements (walls, grounds, objects) from nuclear facilities often suffers from a too small number of measurements. In order to determine risk prediction bounds on the level of contamination,…
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…