Mallows and generalized Mallows model for matchings
type: Item
instance of: scholarly article
title: Mallows and generalized Mallows model for matchings
zbMATH Open document ID: 1423.60025
DOI: 10.3150/17-BEJ1017
author: Ekhine Irurozki
author: Borja Calvo
author: José A. Lozano
published in: Bernoulli
publication date: 2019-04-30T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bj/1551862847
review text: This paper studies the Mallows model, which is an exponential model depending on the definition of a distance for permutations. It is specified by the location parameter \(\sigma_0\) and a dispersion parameter \(\theta\). The generalized Mallows model uses \(k\) spread parameters \(\theta_j\), each affecting a particular position of the permutation. For both Mallows model and the generalized version under the Hamming distance, the paper proposes efficient sampling and learning methods. Expressions for the computation of the partition function of the models, the expectation, the marginal and conditional probabilities are derived. As for the learning process, it is shown the way to estimate the parameters of a sample from a Mallows model in polynomial time. The paper proposes an efficient learning algorithm and shows that the estimated parameters are asymptotically unbiased estimators of the real ones. Numerical examples are provided to illustrate the theoretical results.
reviewed by: Yilun Shang
Mathematics Subject Classification ID: 60C05
Mathematics Subject Classification ID: 05D15
Mathematics Subject Classification ID: 62F10
Mathematics Subject Classification ID: 62H20
zbMATH DE Number: 7049403
zbMATH Keywords: Mallows model
zbMATH Keywords: Hamming distance
zbMATH Keywords: learning
zbMATH Keywords: matching
describes a project that uses: OEIS
describes a project that uses: PerMallows
MaRDI profile type: Publication
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OpenAlex ID: W2921082510
description: scientific article; zbMATH DE number 7049403