Mixture decompositions of exponential families using a decomposition of their sample spaces

Title:

Mixture decompositions of exponential families using a decomposition of their sample spaces

Creator:

Montúfar, Guido F.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:bd2bda1f-748e-4bd1-b15d-0ce5d0e3925f
uuid:bd2bda1f-748e-4bd1-b15d-0ce5d0e3925f

Subject:

mixture model, non-negative tensor rank, perfect code, and marginal polytope

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We study the problem of finding the smallest m such that every element of an exponential family can be written as a mixture of m elements of another exponential family. We propose an approach based on coverings and packings of the face lattice of the corresponding convex support polytopes and results from coding theory. We show that m=qN−1 is the smallest number for which any distribution of N q-ary variables can be written as mixture of m independent q-ary variables. Furthermore, we show that any distribution of N binary variables is a mixture of m=2N−(k+1)(1+1/(2k−1)) elements of the k-interaction exponential family.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

[23]-39

Source:

Kybernetika | 2013 Volume:49 | Number:1

Harvested from:

CDK

Metadata only:

false