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Sharpening jensen's inequality

http://personal.psu.edu/asb17/papers2/Liao,Berg_2024_The-American-Statistician.pdf 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 …

On a Lower Bound for the Jensen Inequality SIAM Journal on ...

Webb28 apr. 2024 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site 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. inducement meaning mifid https://ciclosclemente.com

SharpeningJensen’sInequality

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 Webbvide 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. 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 … inducement in forex pdf

Sharpening Jensen

Category:A Gentle Introduction to Jensen’s Inequality - Machine …

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Sharpening jensen's inequality

[1707.08644] Sharpening Jensen

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 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 …

Sharpening jensen's inequality

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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 … WebbNow, by Jensen’s inequality with weights 1 = = n= 1 n, we have 1 n x 1 p 1 x 1 + x 2 p 1 x 2 + + x n p 1 x n f x 1 + x 2 + + x n n = f 1 n = 1=n p 1 1=n which simpli es to the inequality we wanted. 2.4 The AM-GM inequality The rst example we did can be generalized to a result called the AM-GM (Arithmetic Mean-Geometric Mean) inequality. It ...

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 … 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.

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. … Webbelifesciences.org

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.

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 … inducement small bribeWebbThis 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, … log4j scanning toolsWebbIn 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 inducement of breach of contract