Some properties of Rényi entropy and Rényi entropy rate

Golshani, Leila; Pasha, Einollah; Yari, Gholamhossein

doi:10.1016/j.ins.2009.03.002

Cited by 83 publications

(60 citation statements)

References 29 publications

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“…One can mention, for instance, ecology, quantum information, the Heisenberg XY spin chain model, theoretical computer science, conformal field theory, quantum quenching, diffusion processes, etc. As a small sample, see for example, [1,2,3,4,5,6,7,8,9,10].…”

Section: Introductionmentioning

confidence: 99%

Troublesome aspects of the Renyi-MaxEnt treatment

2016

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We study in great detail the possible existence of a Renyi-associated thermodynamics, with negative results. In particular, we uncover a hidden relation in the Renyi's variational problem (MaxEnt). This relation connects the two associated Lagrange multipliers (Canonical Ensemble) with the mean energy < U > and the Renyi parameter α. As a consequence of such relation, we obtain anomalous RenyiMaxEnt thermodynamic results.

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Section: Introductionmentioning

confidence: 99%

Troublesome aspects of the Renyi-MaxEnt treatment

2016

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“…Moreover, ifᾱ := sup{α : D α (Q P ) < ∞} andᾱ > 1 then D α (Q P ) is finite and continuous on [1,ᾱ). For extension to α ∈ R and many other useful properties of the divergence, see [9], [12], [17] and [18]. The well-known convex duality between exponential integrals and KL divergence [6] states that for any bounded measurable function g : S → R, and every Q ∈ P, ln e g dQ = sup…”

Section: Rényi Divergence and The Lpcbmentioning

confidence: 99%

“…Inequalities (8) and (9) are referred to in [2] as the risk-sensitive functionals comparison bound and logarithmic probability comparison bound, respectively. It is important to mention that both inequalities are tight in the sense that given Q and g, there exists a (unique) measure, namely dP = e αg dQ/Z, Z = e αg dQ, for which (8) holds with equality.…”

Section: Rényi Divergence and The Lpcbmentioning

confidence: 99%

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Information-theoretic applications of the logarithmic probability comparison bound

Atar

Merhav

2015

2015 IEEE International Symposium on Information Theory (ISIT)

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A well-known technique in estimating probabilities of rare events in general and in information theory in particular (used, e.g., in the sphere-packing bound), is that of finding a reference probability measure under which the event of interest has probability of order one and estimating the probability in question by means of the Kullback-Leibler divergence. A method has recently been proposed in [2], that can be viewed as an extension of this idea in which the probability under the reference measure may itself be decaying exponentially, and the Rényi divergence is used instead. The purpose of this paper is to demonstrate the usefulness of this approach in various information-theoretic settings. For the problem of channel coding, we provide a general methodology for obtaining matched, mismatched and robust error exponent bounds, as well as new results in a variety of particular channel models. Other applications we address include rate-distortion coding and the problem of guessing.

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“…S R is considered an important quantifier in variegated areas of science, for instance, ecology, quantum information, Heisenberg's XY spin chain model, theoretical computing, conformal field theory, quantum quenching, diffusion processes, etc. [4,5,6,7,8,9,10,11,12,13,14,15]. Also, the Renyi entropy is important in statistics as indicator of diversity.…”

Section: Introductionmentioning

confidence: 99%