Displaying similar documents to “The analogues of entropy and of Fisher's information measure in free probability theory, II.”

A note on how Rényi entropy can create a spectrum of probabilistic merging operators

Martin Adamčík (2019)

Kybernetika

Similarity:

In this paper we present a result that relates merging of closed convex sets of discrete probability functions respectively by the squared Euclidean distance and the Kullback-Leibler divergence, using an inspiration from the Rényi entropy. While selecting the probability function with the highest Shannon entropy appears to be a convincingly justified way of representing a closed convex set of probability functions, the discussion on how to represent several closed convex sets of probability...

The entropy of algebraic actions of countable torsion-free abelian groups

Richard Miles (2008)

Fundamenta Mathematicae

Similarity:

This paper is concerned with the entropy of an action of a countable torsion-free abelian group G by continuous automorphisms of a compact abelian group X. A formula is obtained that expresses the entropy in terms of the Mahler measure of a greatest common divisor, complementing earlier work by Einsiedler, Lind, Schmidt and Ward. This leads to a uniform method for calculating entropy whenever G is free. In cases where these methods do not apply, a possible entropy formula is conjectured....

Fiber entropy and conditional variational principles in compact non-metrizable spaces

Tomasz Downarowicz, Jacek Serafin (2002)

Fundamenta Mathematicae

Similarity:

We consider a pair of topological dynamical systems on compact Hausdorff (not necessarily metrizable) spaces, one being a factor of the other. Measure-theoretic and topological notions of fiber entropy and conditional entropy are defined and studied. Abramov and Rokhlin's definition of fiber entropy is extended, using disintegration. We prove three variational principles of conditional nature, partly generalizing some results known before in metric spaces: (1) the topological conditional...

Entropy of probability kernels from the backward tail boundary

Tim Austin (2015)

Studia Mathematica

Similarity:

A number of recent works have sought to generalize the Kolmogorov-Sinai entropy of probability-preserving transformations to the setting of Markov operators acting on the integrable functions on a probability space (X,μ). These works have culminated in a proof by Downarowicz and Frej that various competing definitions all coincide, and that the resulting quantity is uniquely characterized by certain abstract properties. On the other hand, Makarov has shown that this...

A pragmatic uncertainty measure based on rate-distortion theory and the uncertainty of BOE's.

Anna Fioretto, Andrea Sgarro (1996)

Mathware and Soft Computing

Similarity:

We discuss pragmatic information measures (hypergraph entropy and fractional entropy) inspired by source-coding theory (rate-distortion theory). We re-phrase the problem in the language of evidence theory, by expressing the pragmatic requirements of the human agent in terms of suitable bodies of evidence, or BOE's. We tackle the situation when the overall uncertainty is removed in two steps. In the case when fractional entropy measures the first-step (partial, pragmatic) uncertainty,...