Results 11 to 20 of about 216,912 (262)
Recoverability for optimized quantum f-divergences [PDF]
Journal of Physics A: Mathematical and Theoretical, 2021 The optimized quantum $f$-divergences form a family of distinguishability measures that includes the quantum relative entropy and the sandwiched R nyi relative quasi-entropy as special cases. In this paper, we establish physically meaningful refinements of the data-processing inequality for the optimized $f$-divergence.
Li Gao, Mark M Wilde
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Some $f$-Divergence Measures Related to Jensen's One
Universal Journal of Mathematics and Applications, 2023 In this paper, we introduce some $f$-divergence measures that are related to the Jensen's divergence introduced by Burbea and Rao in 1982. We establish their joint convexity and provide some inequalities between these measures and a combination of Csisz\'
Sever Dragomır
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Generalized Csiszár's f-divergence for Lipschitzian functions [PDF]
Mathematical Inequalities & Applications, 2021 We started with the generalization of the Csisz ́ar’s f -divergence. We stated and proved Jensen’s type inequality for L-Lipschitzian functions. The results for commonly used examples of f-divergences, such as the Kullbach-Leibler divergence, the Hellinger divergence, the R ́enyi divergence and χ2 -distance are derived.
Pečarić D., Pečarić J., Pokaz D.
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Quadratic Quasinorm and Its Applications in Risk Analysis
Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, 2021 This paper deals with the estimation of the probability distribution of the category random variable from its observed values. The gradient estimation presented is based on the f-quasi-norm term.
Jakub Šácha +2 more
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F-Divergences and Cost Function Locality in Generative Modelling with Quantum Circuits
Entropy, 2021 Generative modelling is an important unsupervised task in machine learning. In this work, we study a hybrid quantum-classical approach to this task, based on the use of a quantum circuit born machine. In particular, we consider training a quantum circuit
Chiara Leadbeater +3 more
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Reviews in Mathematical Physics, 2023 The main result in this paper shows that the quantum [Formula: see text]-divergence of two states is equal to the classical [Formula: see text]-divergence of the corresponding Nussbaum–Szkoła distributions. This provides a general framework for studying certain properties of quantum entropic quantities using the corresponding classical entities.
Androulakis, George, John, Tiju Cherian
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Joint range of f-divergences [PDF]
2010 IEEE International Symposium on Information Theory, 2010 We provide a general method for evaluation of the joint range of f-divergences for two different functions f. Via topological arguments we prove that the joint range for general distributions equals the convex hull of the joint range achieved by the distributions on a two-element set.
Harremoës, Peter, Vajda, Igor
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Sharp Inequalities for $f$-Divergences [PDF]
IEEE Transactions on Information Theory, 2014 $f$-divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics and information theory such as Kullback-Leibler divergence, chi-squared divergence, squared Hellinger distance, total variation distance etc.
Guntuboyina, Adityanand +2 more
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On the Converse Jensen-Type Inequality for Generalized f-Divergences and Zipf–Mandelbrot Law
Mathematics, 2022 Motivated by some recent investigations about the sharpness of the Jensen inequality, this paper deals with the sharpness of the converse of the Jensen inequality.
Mirna Rodić
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Imitation Learning as f-Divergence Minimization [PDF]
, 2021 International Workshop on the Algorithmic Foundations of Robotics (WAFR ...
Ke, Liyiming +5 more
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