The Entropy and Crossentropy of Generalized Mallows Models
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913751474634752 |
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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 |
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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 |