Sharpening jensen's inequality

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August undefined, 2024

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. 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 …

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Webb21 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: 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 … implicit tax tax incidence and pretax returns

Estimation of Jensen’s gap through an integral identity with ...

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 … Webb1 Answer. Yes Jensen inequality holds for multiple variable. We can find a general formulation in the mesure theoretic article in Wikipedia. "Let (Ω, A, μ) be a measure space, such that μ (Ω) = 1. If g is a real-valued function that is μ-integrable, and if g is a convex function on the real line. This generalizable for convex function on ... implicit surface modeling methods

A Gentle Introduction to Jensen’s Inequality - Machine …

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. Webband 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 literacy impacts healthWebb10 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 … implicit taxation

"WebbIn this paper we shall show that sharpening Holder’s Inequality can be¨ generalized to sharpen Jensen’s inequality for concave and convex func-tions 1, 4 .wx We shall also sharpen a majorization theorem for concave functions and two sequences or functions when only one of them is monotonic 6 . . wx 2. SHARPENING JENSEN’S INEQUALITY " - Sharpening jensen's inequality

Sharpening jensen's inequality

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. 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. …

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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 … 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

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 … Webb26 juli 2024 · Sharpening Jensen's Inequality J. G. Liao, Arthur Berg This paper proposes a new sharpened version of the Jensen's inequality. The proposed new bound is simple …

WebbJensen’s inequality is a fundamental inequality in mathematics anditunderliesmanyimportantstatisticalproofsandconcepts. … Webb10 dec. 2024 · The 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. Finally, some applications involving various types of f-divergences 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 …

WebbSharpeningJensen’s Inequality J. G. Liao and Arthur Berg Division of Biostatistics and Bioinformatics Penn State University College of Medicine October 26, 2024 Abstract This … implicit teaching vs explicit teachingWebbDragomir, 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 literacy importance to childrenWebb25 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 … literacy importance in educationWebb10 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 … literacy improvement frameworkWebbSharpening 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. literacy improvement planWebbHowever, 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 literacy imagesWebb3 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 … literacy importance