The Entropy and Crossentropy of Generalized Mallows Models

Fuente: arXiv
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Autor principal: Meilă, Marina
Formato: Preprint
Publicado: 2025
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author Meilă, Marina
author_facet Meilă, Marina
contents The Generalized Mallows Model (GMM) is a well known family of models for ranking data. A GMM is a distribution over $\mathbb{S}_n$, the set of permutations of n objects, characterized by a location parameter $σ\in \mathbb{S}_n$, known as central permutation and a set of dispersion parameters $θ_{1:n-1}\in(0,1]$. The GMM shares many properties, such as having sufficient statistics, with exponential models, thus it can be seen as an exponential family with a discrete parameter $σ$. This paper shows that computing entropy, crossentropy and Kullback-Leibler divergence in the the class of GMM is tractable, paving the way for a better understanding of this exponential family.
format Preprint
id arxiv_https___arxiv_org_abs_2503_17521
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The Entropy and Crossentropy of Generalized Mallows Models
Meilă, Marina
Statistics Theory
Data Structures and Algorithms
Computation
The Generalized Mallows Model (GMM) is a well known family of models for ranking data. A GMM is a distribution over $\mathbb{S}_n$, the set of permutations of n objects, characterized by a location parameter $σ\in \mathbb{S}_n$, known as central permutation and a set of dispersion parameters $θ_{1:n-1}\in(0,1]$. The GMM shares many properties, such as having sufficient statistics, with exponential models, thus it can be seen as an exponential family with a discrete parameter $σ$. This paper shows that computing entropy, crossentropy and Kullback-Leibler divergence in the the class of GMM is tractable, paving the way for a better understanding of this exponential family.
title The Entropy and Crossentropy of Generalized Mallows Models
topic Statistics Theory
Data Structures and Algorithms
Computation
url https://arxiv.org/abs/2503.17521