Results 1 to 10 of about 308,452 (217)
Linear and Multilinear Algebra, 2023 In information theory, the well-known log-sum inequality is a fundamental tool which indicates the non-negativity for the relative entropy. In this article, we establish a set of inequalities which are similar to the log-sum inequality involving two functions defined on scalars. The parametric extended log-sum inequalities are shown.
Supriyo Dutta, Shigeru Furuichi
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Log-sum-exp optimization problem subjected to Lukasiewicz fuzzy relational inequalities [PDF]
, 2022 published in 14th international conference of iranian operation ...
Ghodousian, Amin +2 more
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Guaranteed Bounds on Information-Theoretic Measures of Univariate Mixtures Using Piecewise Log-Sum-Exp Inequalities [PDF]
Entropy, 2016 Information-theoretic measures such as the entropy, cross-entropy and the Kullback-Leibler divergence between two mixture models is a core primitive in many signal processing tasks. Since the Kullback-Leibler divergence of mixtures provably does not admit a closed-form formula, it is in practice either estimated using costly Monte-Carlo stochastic ...
Frank Nielsen, Ke Sun
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Matrix concentration inequalities and efficiency of random universal sets of quantum gates [PDF]
Quantum, 2023 For a random set $\mathcal{S} \subset U(d)$ of quantum gates we provide bounds on the probability that $\mathcal{S}$ forms a $\delta$-approximate $t$-design.
Piotr Dulian, Adam Sawicki
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Geometry of log-concave functions: the $$L_p$$ Asplund sum and the $$L_{p}$$ Minkowski problem [PDF]
Calculus of Variations and Partial Differential Equations, 2020 The aim of this paper is to develop a basic framework of the $L_p$ theory for the geometry of log-concave functions, which can be viewed as a functional "lifting" of the $L_p$ Brunn-Minkowski theory for convex bodies.
Niufa Fang, Sudan Xing, Deping Ye
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$O(T^{-1})$ Convergence of Optimistic-Follow-the-Regularized-Leader in Two-Player Zero-Sum Markov Games [PDF]
arXiv.org, 2022 We prove that optimistic-follow-the-regularized-leader (OFTRL), together with smooth value updates, finds an $O(T^{-1})$-approximate Nash equilibrium in $T$ iterations for two-player zero-sum Markov games with full information.
Yuepeng Yang, Cong Ma
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On a geometric combination of functions related to Prékopa–Leindler inequality [PDF]
Mathematika, 2022 We introduce a new operation between nonnegative integrable functions on Rn$\mathbb {R}^n$ , that we call geometric combination; it is obtained via a mass transportation approach, playing with inverse distribution functions.
G. Crasta, I. Fragalà
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Sharper Sub-Weibull Concentrations
Mathematics, 2022 Constant-specified and exponential concentration inequalities play an essential role in the finite-sample theory of machine learning and high-dimensional statistics area. We obtain sharper and constants-specified concentration inequalities for the sum of
Huiming Zhang, Haoyu Wei
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The Ramanujan journal, 2021 Let σ(n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma (n)$$\end{
Christian Axler
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Sum of squared logarithms - an inequality relating positive definite matrices and their matrix logarithm [PDF]
Journal of Inequalities and Applications, 2013 Let y1,y2,y3,a1,a2,a3∈(0,∞) be such that y1y2y3=a1a2a3 and y1+y2+y3≥a1+a2+a3,y1y2+y2y3+y1y3≥a1a2+a2a3+a1a3. Then (logy1)2+(logy2)2+(logy3)2≥(loga1)2+(loga2)2+(loga3)2. This can also be stated in
M. Bîrsan, P. Neff, J. Lankeit
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