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May 2019 Mallows and generalized Mallows model for matchings
Ekhine Irurozki, Borja Calvo, Jose A. Lozano
Bernoulli 25(2): 1160-1188 (May 2019). DOI: 10.3150/17-BEJ1017


The Mallows and Generalized Mallows Models are two of the most popular probability models for distributions on permutations. In this paper, we consider both models under the Hamming distance. This models can be seen as models for matchings instead of models for rankings. These models cannot be factorized, which contrasts with the popular MM and GMM under Kendall’s-$\tau$ and Cayley distances. In order to overcome the computational issues that the models involve, we introduce a novel method for computing the partition function. By adapting this method we can compute the expectation, joint and conditional probabilities. All these methods are the basis for three sampling algorithms, which we propose and analyze. Moreover, we also propose a learning algorithm. All the algorithms are analyzed both theoretically and empirically, using synthetic and real data from the context of e-learning and Massive Open Online Courses (MOOC).


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Ekhine Irurozki. Borja Calvo. Jose A. Lozano. "Mallows and generalized Mallows model for matchings." Bernoulli 25 (2) 1160 - 1188, May 2019.


Received: 1 September 2016; Published: May 2019
First available in Project Euclid: 6 March 2019

zbMATH: 07049403
MathSciNet: MR3920369
Digital Object Identifier: 10.3150/17-BEJ1017

Keywords: Generalized Mallows Model , Hamming , learning , Mallows model , Matching , sampling

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability


Vol.25 • No. 2 • May 2019
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