The Case for Shifting the Renyi Entropy
We introduce a variant of the Rényi entropy definition that aligns it with the well-known Hölder mean: in the new formulation, the r-th order Rényi Entropy is the logarithm of the inverse of the r-th order Hölder mean. This brings about new insights into the relationship of the Rényi entropy to quan...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-01-01
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| Series: | Entropy |
| Subjects: | |
| Online Access: | http://www.mdpi.com/1099-4300/21/1/46 |
| _version_ | 1828348602447036416 |
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| author | Francisco J. Valverde-Albacete Carmen Peláez-Moreno |
| author_facet | Francisco J. Valverde-Albacete Carmen Peláez-Moreno |
| author_sort | Francisco J. Valverde-Albacete |
| collection | DOAJ |
| description | We introduce a variant of the Rényi entropy definition that aligns it with the well-known Hölder mean: in the new formulation, the r-th order Rényi Entropy is the logarithm of the inverse of the r-th order Hölder mean. This brings about new insights into the relationship of the Rényi entropy to quantities close to it, like the information potential and the partition function of statistical mechanics. We also provide expressions that allow us to calculate the Rényi entropies from the Shannon cross-entropy and the escort probabilities. Finally, we discuss why shifting the Rényi entropy is fruitful in some applications. |
| first_indexed | 2024-04-14T00:57:09Z |
| format | Article |
| id | doaj.art-48084133493c4faaa5411c25dde88731 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-14T00:57:09Z |
| publishDate | 2019-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-48084133493c4faaa5411c25dde887312022-12-22T02:21:34ZengMDPI AGEntropy1099-43002019-01-012114610.3390/e21010046e21010046The Case for Shifting the Renyi EntropyFrancisco J. Valverde-Albacete0Carmen Peláez-Moreno1Department of Signal Theory and Communications, Universidad Carlos III de Madrid, 28911 Leganés, SpainDepartment of Signal Theory and Communications, Universidad Carlos III de Madrid, 28911 Leganés, SpainWe introduce a variant of the Rényi entropy definition that aligns it with the well-known Hölder mean: in the new formulation, the r-th order Rényi Entropy is the logarithm of the inverse of the r-th order Hölder mean. This brings about new insights into the relationship of the Rényi entropy to quantities close to it, like the information potential and the partition function of statistical mechanics. We also provide expressions that allow us to calculate the Rényi entropies from the Shannon cross-entropy and the escort probabilities. Finally, we discuss why shifting the Rényi entropy is fruitful in some applications.http://www.mdpi.com/1099-4300/21/1/46shifted Rényi entropyShannon-type relationsgeneralized weighted meansHölder meansescort distributions |
| spellingShingle | Francisco J. Valverde-Albacete Carmen Peláez-Moreno The Case for Shifting the Renyi Entropy Entropy shifted Rényi entropy Shannon-type relations generalized weighted means Hölder means escort distributions |
| title | The Case for Shifting the Renyi Entropy |
| title_full | The Case for Shifting the Renyi Entropy |
| title_fullStr | The Case for Shifting the Renyi Entropy |
| title_full_unstemmed | The Case for Shifting the Renyi Entropy |
| title_short | The Case for Shifting the Renyi Entropy |
| title_sort | case for shifting the renyi entropy |
| topic | shifted Rényi entropy Shannon-type relations generalized weighted means Hölder means escort distributions |
| url | http://www.mdpi.com/1099-4300/21/1/46 |
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