A new group of transformations related to the Kullback–Leibler and Rényi divergences and universal classes of monotone measures of statistical complexity.
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| Title: | A new group of transformations related to the Kullback–Leibler and Rényi divergences and universal classes of monotone measures of statistical complexity. |
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| Authors: | Gabriel Iagar, Razvan1 (AUTHOR) razvan.iagar@urjc.es, Puertas-Centeno, David1,2 (AUTHOR) david.puertas@urjc.es, Toranzo, Elio V1 (AUTHOR) elio.vtoranzo@urjc.es |
| Source: | Journal of Physics A: Mathematical & Theoretical. 2026, Vol. 59 Issue 26, p1-30. 30p. |
| Subjects: | Probability density function, Transformation groups, Statistical measurement, Renyi's entropy, Information theory, Mathematical transformations |
| Abstract: | In this work we introduce a family of transformations, named divergence transformations, interpolating between any pair of probability density functions sharing the same support. We prove the remarkable property that the whole family of Kullback–Leibler and Rényi divergences evolves in a monotone way with respect to the transformation parameter. Moreover, fixing the reference density, we show that the divergence transformations enjoy a group structure and can be derived through the algebraic conjugation of the differential-escort transformations and their relative counterparts. This algebraic structure allows us to deform any density function in such a way its divergence with respect to a fixed reference density might also increase as much as possible. We also establish the monotonicity of composed measures involving the proper Kullback–Leibler and Rényi divergences as well as other relative measures of moment and Fisher types. As applications, an approximation scheme of general density functions by simple functions is provided. In addition, we give a number of analytical and numerical examples of interest in both regimes of increasing and decreasing divergence. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Physics A: Mathematical & Theoretical is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 194972055 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A new group of transformations related to the Kullback–Leibler and Rényi divergences and universal classes of monotone measures of statistical complexity. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Gabriel+Iagar%2C+Razvan%22">Gabriel Iagar, Razvan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> razvan.iagar@urjc.es</i><br /><searchLink fieldCode="AR" term="%22Puertas-Centeno%2C+David%22">Puertas-Centeno, David</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> david.puertas@urjc.es</i><br /><searchLink fieldCode="AR" term="%22Toranzo%2C+Elio+V%22">Toranzo, Elio V</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> elio.vtoranzo@urjc.es</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Physics+A%3A+Mathematical+%26+Theoretical%22">Journal of Physics A: Mathematical & Theoretical</searchLink>. 2026, Vol. 59 Issue 26, p1-30. 30p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Probability+density+function%22">Probability density function</searchLink><br /><searchLink fieldCode="DE" term="%22Transformation+groups%22">Transformation groups</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+measurement%22">Statistical measurement</searchLink><br /><searchLink fieldCode="DE" term="%22Renyi's+entropy%22">Renyi's entropy</searchLink><br /><searchLink fieldCode="DE" term="%22Information+theory%22">Information theory</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+transformations%22">Mathematical transformations</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this work we introduce a family of transformations, named divergence transformations, interpolating between any pair of probability density functions sharing the same support. We prove the remarkable property that the whole family of Kullback–Leibler and Rényi divergences evolves in a monotone way with respect to the transformation parameter. Moreover, fixing the reference density, we show that the divergence transformations enjoy a group structure and can be derived through the algebraic conjugation of the differential-escort transformations and their relative counterparts. This algebraic structure allows us to deform any density function in such a way its divergence with respect to a fixed reference density might also increase as much as possible. We also establish the monotonicity of composed measures involving the proper Kullback–Leibler and Rényi divergences as well as other relative measures of moment and Fisher types. As applications, an approximation scheme of general density functions by simple functions is provided. In addition, we give a number of analytical and numerical examples of interest in both regimes of increasing and decreasing divergence. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Physics A: Mathematical & Theoretical is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1088/1751-8121/ae7c40 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 30 StartPage: 1 Subjects: – SubjectFull: Probability density function Type: general – SubjectFull: Transformation groups Type: general – SubjectFull: Statistical measurement Type: general – SubjectFull: Renyi's entropy Type: general – SubjectFull: Information theory Type: general – SubjectFull: Mathematical transformations Type: general Titles: – TitleFull: A new group of transformations related to the Kullback–Leibler and Rényi divergences and universal classes of monotone measures of statistical complexity. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Gabriel Iagar, Razvan – PersonEntity: Name: NameFull: Puertas-Centeno, David – PersonEntity: Name: NameFull: Toranzo, Elio V IsPartOfRelationships: – BibEntity: Dates: – D: 03 M: 07 Text: 2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 17518113 Numbering: – Type: volume Value: 59 – Type: issue Value: 26 Titles: – TitleFull: Journal of Physics A: Mathematical & Theoretical Type: main |
| ResultId | 1 |
