Sharpening jensen's inequality

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August undefined, 2024

Webb3 juli 2024 · 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 … WebbJensen's inequality is an inequality involving convexity of a function. We first make the following definitions: A function is convex on an interval I I if the segment between any two points taken on its graph ( ( in I) I) lies above the graph. An example of a convex function is f (x)=x^2 f (x) = x2. A function is concave on an interval

A Gentle Introduction to Jensen’s Inequality - Machine …

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 … Webb3 sep. 2024 · 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 the best of our … clint black wife and children

A converse to the Jensen inequality, its matrix extensions and

WebbThe widely used Jensen’s inequality for convex functions, attributed to Danish mathematician Johan Jensen, dates back to 1906[12]. The literature contains numerous bounds on the Jensen gap, deﬁned as J (f,X ∼ P) = E[f (X)] − f (E[X]), where X is a random variable with distribution P, and the function f might be convex or nonconvex [20]. WebbRefinements of Jensen’s Inequality via Majorization Results with Applications in the Information Theory Yongping Deng ,1 Hidayat Ullah ,2 Muhammad Adil Khan ,2 Sajid Iqbal ,3 and Shanhe Wu 1 1DepartmentofMathematics,LongyanUniversity,Longyan364012,China 2DepartmentofMathematics,UniversityofPeshawar,Peshawar25000,Pakistan WebbSharpening 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 … clint black without hat

Inequalities for $$L^p$$ L p -Norms that Sharpen the Triangle ...

WebbJensen's Inequality Continuous Form It Application Interpolation Result We give a refinement of the converse Hölder inequality for functionals using an interpolation result for Jensen’s inequality. Additionally, we obtain similar improvements of the converse of the Beckenbach 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 … bobby patterson musicianWebbJensen’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 for statistics. Let X be a random variable with finite expectation and let φ(x) be a convex function. Jensen’s inequality (Jensen, 1906) establishes: E[φ(X)]− φ(E[X]) ≥ 0. bobby patton fort worth

"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 … " - Sharpening jensen's inequality

Sharpening jensen's inequality

http://ele-math.com/static/pdf/books/17689-MIA19.pdf 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 …

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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 … WebbHowever, applying Jensen on log-sums in Ie and £(XIE» is not as straightforward. Some terms in these expressions involve negative log-sums and so Jensen is actually solving for an upper bound on those terms. If we want overall lower and upper bounds on Ie and £(XIE», we need to compute reverse-Jensen bounds. 5 Reverse-Jensen Bounds

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, … WebbUnder certain conditions, it is an ultimate bound equal to the Jensen gap. To the best of our knowledge, this is the first such bound to be developed. The proposed bound is applied to moment generating functions, the inequality of arithmetic and geometric means, a power mean, and information entropy.

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 functions and considering the case of the real Stieltjes measure, not necessarily positive.

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.

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. … clint black wife of 1991WebbSharpeningJensen’s Inequality J. G. Liao and Arthur Berg Division of Biostatistics and Bioinformatics Penn State University College of Medicine October 26, 2024 Abstract This … clint black wife diedWebbDive 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 ... clint black wife and kidsWebb至于《数学分析》中对于函数凹凸的定义，也是由于历史原因有诸多版本。. 有兴趣的读者可以看看数学分析，而本文更侧重于Jensen inequality. 我们说. f（x）’>0\Leftrightarrow f（x）函数增. f（x）’<0\Leftrightarrow f（x）函数减. 以上内容初一甚至更早大家已经有所 … bobby patton fort worth txWebb19 nov. 2024 · Jensen's inequality的背景是独特的形象化的。但凡看的的懂图像的人，都能从函数图像上直观的感受到这个不等式是自然成立的，而这正是优秀的数学工作的特点——简洁而不平凡。通过它还可证明基本不等式，只需构造简单的函数关系即可，非常简单明了。除了居高临下看过往，它还可高瞻远瞩建桥梁。 Young's inequality也可 … bobby patton jrWebbIn this paper we introduce a new mapping connected with the classical inequality due to Jensen and point out its main properties. Some applications related to well-known inequalities are also established. bobby patton ranchesWebbvide a more general reﬁnement of integral Jensen’s inequality. We establish a reﬁnement of discrete Jensen’s inequality concerning certain tuples and give applications to different means. Finally, we give applications of discrete main result in information theory and providea more generalreﬁnement of discrete Jensen’s inequality. bobby paul bryer