Sharpening jensen's inequality

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August undefined, 2024

Webb1 sep. 2024 · This post is all about Jensen’s inequality, an elementary but powerful result about convex functions. It comes up all over the place in mathematics, probably because the concept of convexity is itself so fundamental. I ran into it recently as I was thinking about relative entropy and why it is so well behaved; I think a lot of it comes down to the … http://personal.psu.edu/asb17/papers2/Liao,Berg_2024_The-American-Statistician.pdf

About the sharpness of the Jensen inequality - PubMed

WebbJensen’s inequality is covered in all major statistical textbooks such as Casella and Berger ( 2002, Section 4.7) and Wasserman ( 2013, Section 4.2) as a basic mathematical tool … WebbThis article proposes a new sharpened version of Jensen's inequality. The proposed new bound is simple and insightful, is broadly applicable by imposing minimum assumptions, … cie tours heritage

Sharpening Jensen

Webb25 maj 2024 · The proof of Proposition 3.1 is based on Jensen’s inequality, but the reduction to constants is not obtained by applying Jensen’s inequality to show that … WebbIn particular, just as the Jensen inequality becomes an equality when ϕ is linear, for the new inequality we obtain an equality also when ϕ is quadratic. At the heart of the paper is an apparent new technique for improving classical inequalities based on nonlinear functions. MSC codes analytic function convex function Jensen gap power series Webb12 nov. 2024 · The Jensen inequality is a widely used tool in a multitude of fields, such as for example information theory and machine learning. It can be also used to derive other standard inequalities such as the inequality of arithmetic and geometric means or the Hölder inequality. cie tours taste of britain

Sharpening Jensen

WebbDragomir, Sever S ORCID: 0000-0003-2902-6805 (2024) Refining Jensen's Integral Inequality for Partition of Weights. Libertas Mathematica (new series), 37 (1). 25 - 44. ISSN 0278-5307 WebbThe main aim of this paper is to give an improvement of the recent result on the sharpness of the Jensen inequality. The results given here are obtained using different Green … dhanush remunerationIn mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function. It was proved by Jensen in 1906, building on an earlier proof of the same inequality for doubly-differentiable functions by Otto Hölder … Visa mer The classical form of Jensen's inequality involves several numbers and weights. The inequality can be stated quite generally using either the language of measure theory or (equivalently) probability. In the … Visa mer Form involving a probability density function Suppose Ω is a measurable subset of the real line and f(x) is a non-negative function such that $${\displaystyle \int _{-\infty }^{\infty }f(x)\,dx=1.}$$ Visa mer • Jensen's Operator Inequality of Hansen and Pedersen. • "Jensen inequality", Encyclopedia of Mathematics, EMS Press, 2001 [1994] • Weisstein, Eric W. "Jensen's inequality". MathWorld. Visa mer Jensen's inequality can be proved in several ways, and three different proofs corresponding to the different statements above will be offered. Before embarking on these … Visa mer • Karamata's inequality for a more general inequality • Popoviciu's inequality • Law of averages • A proof without words of Jensen's inequality Visa mer dhanush recent movie name

"Webb10 nov. 2024 · Abstract and Figures In this study, we propose a new bound for Jensen's inequality. Under certain conditions, it is an ultimate bound equal to the Jensen gap. To … " - Sharpening jensen's inequality

Sharpening jensen's inequality

(PDF) About the sharpness of the Jensen inequality

Webb18 dec. 2024 · The prime purpose of this paper is to provide a refinement of Jensen’s inequality in connection with a positive finite sequence. We deal with the refinement for particular cases and point out the relation between the new result with earlier results of Jensen’s inequality. As results, we obtain refinements of the …

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WebbSharpening Jensen's Inequality Published in: The American Statistician, June 2024 DOI: 10.1080/00031305.2024.1419145: Authors: J. G. Liao, Arthur Berg View on publisher site Alert me about new mentions. Twitter Demographics. The data shown below were collected from the profiles of 4 tweeters who shared this research output. WebbJensen’s inequality is a fundamental inequality in mathematics anditunderliesmanyimportantstatisticalproofsandconcepts. …

Webb10 dec. 2024 · The Jensen inequality is one of the most famous and most important inequalities in math- ematical analysis. In [ 2 ], some estimates about the sharpness of … WebbDive into the research topics of 'Sharpening Jensen's Inequality'. Together they form a unique fingerprint. Sort by Weight Alphabetically Mathematics. Jensen's inequality 74%. Power Mean 38%. Moment generating function 34%. Presentation 24%. Calculus 23%. Form 12%. Business & Economics. Jensen's Inequality 100%. Moment ...

Webb4 sep. 2024 · In recent years, many researchers have been interested in studying the mathematical equivalence among some famous analytical inequalities, such as the Cauchy–Schwarz inequality, the Bernoulli inequality, the Wielandt inequality, and the Minkowski inequality; see [7,8,9,10,11,12,13] for details.Additionally, these studies note … Webb本文旨在以非常简短易懂的方式介绍一下Jensen's Inequality与KL散度，这两部分内容是机器学习中很多模型的基础内容之一，了解它们是掌握更加复杂的机器学习算法的必要要求。相关基础知识：高等数学中的函数插值，对数运算，概率论中的期望定义. …

Webb6 dec. 2024 · J. Liao and A. Berg. Sharpening Jensen's inequality. The American Statistician, 73 (3):278–281, 2024. J. Liu, J. Paisley, M.- A. Kioumourtzoglou, and B. Coull. Accurate uncertainty estimation and decomposition in ensemble learning. In Advances in Neural Information Processing Systems, pages 8950–8961, 2024.

WebbThis paper proposes a new sharpened version of the Jensen's inequality. The proposed new bound is simple and insightful, is broadly applicable by imposing minimum … cie tours to icelandWebb21 juli 2024 · And I carefully reviewed proof process of Jensen's Inequality and found Why "Jensen's inequality Do Not hold in general finite measure space". I write this thought down for anyone who has the same confusion. In the original Proof: Proof: cie tours stand forWebband its reverse version. We also sharpen Jensen's inequalities for positive isotonic linear functionals. 1. Introduction. In the articles [1] and [2] sharpenings of the inte-gral versions of Holder's and Jensen's inequalities were obtained. Here we improve these results using a positive isotonic functional leading cie tours southern gemsWebbSharpening Jensen's Inequality Liao, J. G. ; Berg, Arthur This paper proposes a new sharpened version of the Jensen's inequality. The proposed new bound is simple and insightful, is broadly applicable by imposing minimum assumptions, and provides fairly accurate result in spite of its simple form. cie travel tours reviewsWebbFurther sharpening of Jensen's inequality Sang Kyu Lee a Department of Statistics and Probability, Michigan State University, East Lansing, MI, USA View further author … dhanush relation with rajinikanthWebb3 sep. 2024 · Jensen’s Inequality is a useful tool in mathematics, specifically in applied fields such as probability and statistics. For example, it is often used as a tool in … cie tours taste of wales and irelandWebbSharpening Jensen's Inequality. J. G. Liao and Arthur Berg. The American Statistician, 2024, vol. 73, issue 3, 278-281 . Abstract: This article proposes a new sharpened version of Jensen's inequality. The proposed new bound is simple and insightful, is broadly applicable by imposing minimum assumptions, and provides fairly accurate results in spite of its … ciet retscreen training