Mallows and generalized Mallows model for matchings

The Mallows and Generalized Mallows Models are two of the most popular probability models for distribu- tions 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 fac...

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Detalles Bibliográficos
Autores: Irurozki, E., Calvo, B., Lozano, J.A.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2019
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/942
Acceso en línea:http://hdl.handle.net/20.500.11824/942
Access Level:acceso abierto
Palabra clave:Generalized Mallows Model
hamming
learning
Mallows Model
matching
sampling
Descripción
Sumario:The Mallows and Generalized Mallows Models are two of the most popular probability models for distribu- tions 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-τ 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).