Congruent Families and Invariant Tensors

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F18%3A00497781" target="_blank" >RIV/67985840:_____/18:00497781 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1007/978-3-319-97798-0_6" target="_blank" >http://dx.doi.org/10.1007/978-3-319-97798-0_6</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-319-97798-0_6" target="_blank" >10.1007/978-3-319-97798-0_6</a>

Result language

angličtina

Original language name

Congruent Families and Invariant Tensors

Original language description

Classical results of Chentsov and Campbell state that -- up to constant multiples -- the only 2-tensor field of a statistical model which is invariant under congruent Markov morphisms is the Fisher metric and the only invariant 3-tensor field is the Amari-Chentsov tensor. We generalize this result for arbitrary degree n, showing that any family of n-tensors which is invariant under congruent Markov morphisms is algebraically generated by the canonical tensor fields defined in an earlier paper.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

<a href="/en/project/GC18-01953J" target="_blank" >GC18-01953J: Geometric methods in statistical learning theory and applications</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2018

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

Information Geometry and Its Applications

ISBN

978-3-319-97797-3

ISSN

2194-1009

e-ISSN

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Number of pages

31

Pages from-to

157-187

Publisher name

Springer

Place of publication

Cham

Event location

Liblice

Event date

Jun 12, 2016

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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