Geodesic
Multi-variate correlation and mixtures of product measures
Kybernetika, Tome 56 (2020) no. 3, pp. 459-499.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Total correlation (`TC') and dual total correlation (`DTC') are two classical ways to quantify the correlation among an $n$-tuple of random variables. They both reduce to mutual information when $n=2$. The first part of this paper sets up the theory of TC and DTC for general random variables, not necessarily finite-valued. This generality has not been exposed in the literature before. The second part considers the structural implications when a joint distribution $\mu$ has small TC or DTC. If $\mathrm{TC}(\mu) = o(n)$, then $\mu$ is close to a product measure according to a suitable transportation metric: this follows directly from Marton's classical transportation-entropy inequality. If $\mathrm{DTC}(\mu) = o(n)$, then the structural consequence is more complicated: $\mu$ is a mixture of a controlled number of terms, most of them close to product measures in the transportation metric. This is the main new result of the paper.
DOI : 10.14736/kyb-2020-3-0459
Classification : 60B99, 60G99, 62B10, 94A17
Keywords: total correlation; dual total correlation; transportation inequalities; mixtures of products 
@article{10_14736_kyb_2020_3_0459,
     author = {Austin, Tim},
     title = {Multi-variate correlation and mixtures of product measures},
     journal = {Kybernetika},
     pages = {459--499},
     publisher = {mathdoc},
     volume = {56},
     number = {3},
     year = {2020},
     doi = {10.14736/kyb-2020-3-0459},
     mrnumber = {4131739},
     zbl = {07250733},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2020-3-0459/}
}
TY  - JOUR
AU  - Austin, Tim
TI  - Multi-variate correlation and mixtures of product measures
JO  - Kybernetika
PY  - 2020
SP  - 459
EP  - 499
VL  - 56
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2020-3-0459/
DO  - 10.14736/kyb-2020-3-0459
LA  - en
ID  - 10_14736_kyb_2020_3_0459
ER  - 
%0 Journal Article
%A Austin, Tim
%T Multi-variate correlation and mixtures of product measures
%J Kybernetika
%D 2020
%P 459-499
%V 56
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2020-3-0459/
%R 10.14736/kyb-2020-3-0459
%G en
%F 10_14736_kyb_2020_3_0459
Austin, Tim. Multi-variate correlation and mixtures of product measures. Kybernetika, Tome 56 (2020) no. 3, pp. 459-499. doi : 10.14736/kyb-2020-3-0459. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2020-3-0459/

Cité par Sources :