Related papers: A Reverse Jensen Inequality Result with Applicatio…
This work studies the Geometric Jensen-Shannon divergence, based on the notion of geometric mean of probability measures, in the setting of Gaussian measures on an infinite-dimensional Hilbert space. On the set of all Gaussian measures…
A real valued function defined on}$\mathbb{R}$ {\small is called}$g${\small --convex if it satisfies the following \textquotedblleft generalized Jensen's inequality\textquotedblright under a given}$g${\small -expectation, i.e.,…
We give a general formulation of Jensen's operator inequality for unital fields of positive linear mappings, and we consider different types of converse inequalities.
The Reverse Stein Effect is identified and illustrated: A statistician who shrinks his/her data toward a point chosen without reliable knowledge about the underlying value of the parameter to be estimated but based instead upon the observed…
In inverse problems, one attempts to infer spatially variable functions from indirect measurements of a system. To practitioners of inverse problems, the concept of "information" is familiar when discussing key questions such as which parts…
We prove certain type symmetric inequalities in $\textbf{R}^{2}$ and $\textbf{R}^3$, that ocur in many problems of analysis. These inequalities are generalizations of the Jensen's inequality from one variable to two and three variables
We discuss a rather general condition under which the inequality of Jensen works for certain convex combinations of points not all in the domain of convexity of the function under attention. Based on this fact, an extension of the…
We introduce a comprehensive method for establishing stochastic orders among order statistics in the i.i.d. case. This approach relies on the assumption that the underlying distribution is linked to a reference distribution through a…
The consensus problem -- achieving agreement among a network of agents -- is a central theme in both theory and applications. Recently, this problem has been extended from Euclidean spaces to the space of probability measures, where the…
We establish in this paper some inequalities for analytic and convex functions on an open interval and positive normalized functionals defined on a Hermitian unital Banach *-algebra. Reverses and refinements of Jensen's and Slater's type…
The aim of this paper is to present some new Fejer-type results for convex functions. Improvements of Young's inequality (the arithmetic-geometric mean inequality) and other applications to special means are pointed as well.
In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, root square mean, etc. Considering the difference of these means, we can establish. some inequalities among them. Interestingly, the difference of…
Deep learning based physical layer design, i.e., using dense neural networks as encoders and decoders, has received considerable interest recently. However, while such an approach is naturally training data-driven, actions of the wireless…
The main goal of this article is to find the exact difference between a convex function and its secant, as a limit of positive quantities. This idea will be expressed as a convex inequality that leads to refinements and reversals of well…
Generalization error bounds are essential to understanding machine learning algorithms. This paper presents novel expected generalization error upper bounds based on the average joint distribution between the output hypothesis and each…
It is shown that, for open sets in classical potential theory and - more generally - for elliptic harmonic spaces, the set of Jensen measures for a point is a simple union of closed faces of a compact convex set which has been thoroughly…
The measure of Jensen-Fisher divergence between probability distributions is introduced and its theoretical grounds set up. This quantity, in contrast to the remaining Jensen divergences, is very sensitive to the fluctuations of the…
We introduce a divergence measure between data distributions based on operators in reproducing kernel Hilbert spaces defined by kernels. The empirical estimator of the divergence is computed using the eigenvalues of positive definite Gram…
In this paper, we prove an operator version of the Jensen's inequality and its converse for $h$-convex functions. We provide a refinement of the Jensen type inequality for $h$-convex functions. Moreover, we prove the Hermite-Hadamard's type…
The present paper is devoted to the study of Jensen-Mercer-type inequalities. Our results generalize and improve some earlier results in the literature.