# Weighted Approach to R\'enyi Entropy

@inproceedings{mieja2012WeightedAT, title={Weighted Approach to R\'enyi Entropy}, author={Marek Śmieja and Jacek Tabor}, year={2012} }

Rényi entropy of order α is a general measure of entropy. In this paper we derive estimations for the Rényi entropy of the mixture of sources in terms of the entropy of the single sources. These relations allow to compute the Rényi entropy dimension of arbitrary order of a mixture of measures. The key for obtaining these results is our new definition of the weighted Rényi entropy. It is shown that weighted entropy is equal to the classical Rényi entropy.

## Topics from this paper

## References

SHOWING 1-10 OF 20 REFERENCES

A Coding Theorem and Rényi's Entropy

- Mathematics, Computer ScienceInf. Control.
- 1965

It is shown that L(t) has some desirable properties as a measure of typical code length and a coding theorem for a noiseless channel is proved.

Estimation of the Kolmogorov entropy from a chaotic signal

- Physics
- 1983

While there has been recently a dramatic growth in new mathematical concepts related to chaotic systems, ' the detailed comparison between models and experimental data has lagged somewhat. After…

Algorithmic information theory

- Computer Science, MathematicsScholarpedia
- 2007

This article is a brief guide to the field of algorithmic information theory, its underlying philosophy, the major subfields, applications, history, and a map of the field are presented.

Entropy and Information Theory

- MathematicsSpringer New York
- 1990

This book is an updated version of the information theory classic, first published in 1990. About one-third of the book is devoted to Shannon source and channel coding theorems; the remainder…

Rényi Information Dimension: Fundamental Limits of Almost Lossless Analog Compression

- Mathematics, Computer ScienceIEEE Transactions on Information Theory
- 2010

Almost lossless analog compression for analog memoryless sources in an information-theoretic framework, in which the compressor or decompressor is constrained by various regularity conditions, in particular linearity of the compressor and Lipschitz continuity of the decompressor.

Epsilon entropy of stochastic processes.

- Mathematics
- 1967

Epsilon-delta entropy for probabilistic metric spaces applied to stochastic processes in data transmission

A Mathematical Theory of Communication

- 2006

This paper opened the new area the information theory. Before this paper, most people believed that the only way to make the error probability of transmission as small as desired is to reduce the…

Entropy of the Mixture of Sources and Entropy Dimension

- Mathematics, Computer ScienceIEEE Transactions on Information Theory
- 2012

The basic role is played by a new equivalent definition of entropy based on measures instead of partitions, which decomposes the entropy dimension of the mixture of sources in terms of the convex combination of the entropy dimensions of the single sources.

Entropy, large deviations, and statistical mechanics

- Mathematics
- 1985

I: Large Deviations and Statistical Mechanics.- I. Introduction to Large Deviations.- I.1. Overview.- I.2. Large Deviations for I.I.D. Random Variables with a Finite State Space.- I.3. Levels-1 and 2…

Convex Functions and Their Applications: A Contemporary Approach

- Computer Science
- 2005

This second edition provides a thorough introduction to contemporary convex function theory with many new results. A large variety of subjects are covered, from the one real variable case to some o…