Sharpening jensen's inequality

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August undefined, 2024

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, … WebbWe obtain a scalar inequality, converse to the Jensen inequality. We also derive an op-erator converse to the Jensen inequality. As special cases, we obtain inequalities, similar to the Kantorovich one as well as some operator generalizations of them. Using some exterior algebra, we prove a generalization of the Sylvester determinant theorem.

About the sharpness of the Jensen inequality - PubMed

WebbIn this article, we consider the generalized forms of the Jensen's inequality given by Jessen and McShane for isotonic linear functionals, derive several refinements for the Jessen's and McShane's inequalities connected to certain functions from the linear space, generalize the Jessen's and McShane's inequalities pertaining n certain functions. WebbJensen’s inequality is a fundamental inequality in mathematics anditunderliesmanyimportantstatisticalproofsandconcepts. … how many seasons will euphoria have

Altmetric – Sharpening Jensen

WebbThe inequality (1.5)is appropriate for iteration, using a sequence of functions. e. 1, e. 2, e. 3, ..., as in the case of Bessel’s inequality, but if. c. θ,r < 1 there is an exponential decay of the coeﬃcients in the analogue of Bessel’s inequality. We note that the inequality (1.5)holds trivially for. c. θ,r =0by Hölder’s inequality ... WebbSharpening 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. WebbProving Holder's inequality using Jensen's inequality. Asked 9 years, 4 months ago. Modified 7 years, 11 months ago. Viewed 5k times. 6. Let p and q be positive reals such … how did food insecurity start

A converse to the Jensen inequality, its matrix extensions and

Webb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 … WebbSharpening 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 … how many seasons will mha haveWebbJensen’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. how did food rationing work

"Webb琴生不等式（英語： Jensen's inequality ，台湾稱作簡森不等式 [1] ），或稱延森不等式，以丹麥數學家約翰·延森命名。它給出積分的凸函數值和凸函數的積分值間的關係，在此不等式最簡單形式中，闡明了對一平均做凸函數轉換，會小於等於先做凸函數轉換再平均。若將簡森不等式應用在二點上，就回到了凸函數的基本性質：过一个凸函数上任意 … " - Sharpening jensen's inequality

Sharpening jensen's inequality

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. Webb19 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 …

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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 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 …

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 … 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 …

WebbSharpening Jensen's Inequality J. Liao, Arthur Berg Mathematics The American Statistician 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 minimum assumptions, and provides… Expand 50 PDF View 1 excerpt, references background 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 …

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.

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 … how many seasons will legacies haveWebbReduce inequality within and among countries - United Nations Sustainable Development. Home. About. Goals. Take Action. Partnerships. News and Media. Learn more. UN 2024 Water Conference. how many seasons will mushoku tensei haveWebbHowever, 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 how did foodpanda startWebbRefinements 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 how did food surpluses change the way of lifeWebb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. … how did food surplus stimulate tradeWebband 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 how did food stamps begin how did food production aid industrialization