منابع مشابه
A variational characterization of Rényi divergences
Atar, Chowdhary and Dupuis have recently exhibited a variational formula for exponential integrals of bounded measurable functions in terms of Rényi divergences. We develop a variational characterization of the Rényi divergences between two probability distributions on a measurable space in terms of relative entropies. When combined with the elementary variational formula for exponential integr...
متن کاملAPPROXIMATION AND ESTIMATION OF s-CONCAVE DENSITIES VIA RÉNYI DIVERGENCES.
In this paper, we study the approximation and estimation of s-concave densities via Rényi divergence. We first show that the approximation of a probability measure Q by an s-concave density exists and is unique via the procedure of minimizing a divergence functional proposed by [Ann. Statist.38 (2010) 2998-3027] if and only if Q admits full-dimensional support and a first moment. We also show c...
متن کاملOn Rényi and Tsallis entropies and divergences for exponential families
Many common probability distributions in statistics like the Gaussian, multinomial, Beta or Gamma distributions can be studied under the unified framework of exponential families. In this paper, we prove that both Rényi and Tsallis divergences of distributions belonging to the same exponential family admit a generic closed form expression. Furthermore, we show that Rényi and Tsallis entropies c...
متن کاملRényi divergences as weighted non-commutative vector valued $L_p$-spaces
We show that Araki and Masuda’s weighted non-commutative vector valued Lp-spaces [Araki & Masuda, Publ. Res. Inst. Math. Sci., 18:339 (1982)] correspond to an algebraic generalization of the sandwiched Rényi divergences with parameter α = p 2 . Using complex interpolation theory, we prove various fundamental properties of these divergences in the setup of von Neumann algebras, including a data ...
متن کاملCoding Theorems for Compound Problems via Quantum Rényi Divergences
We show two-sided bounds between the traditional quantum Rényi divergences and the new notion of Rényi divergences introduced recently in Müller-Lennert, Dupuis, Szehr, Fehr and Tomamichel, J. Math. Phys. 54, 122203, (2013), and Wilde, Winter, Yang, arXiv:1306.1586. The bounds imply that the two versions can be used interchangeably near α = 1, and hence one can benefit from the best properties ...
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ژورنال
عنوان ژورنال: Journal of High Energy Physics
سال: 2020
ISSN: 1029-8479
DOI: 10.1007/jhep04(2020)094