Title: Efficient and accurate inference for mixtures of Mallows models with Spearman distance Authors:  Cristina Mollica - Sapienza Universita di Roma (Italy)
Valerio Astuti - Bank of Italy (Italy)
Luca Tardella - Sapienza University of Rome (Italy)
Marta Crispino - Bank of Italy (Italy) [presenting]
Abstract: The Mallows model occupies a central role in the parametric modelling of ranking data to learn the preferences of a population of judges. Despite the wide range of metrics for rankings that can be considered in the model specification, the choice is typically limited to the Kendall, Cayley or Hamming distances due to the closed-form expression of the related model normalizing constant. Instead, the focus is on the Mallows model with Spearman distance. An efficient and accurate EM algorithm for estimating finite mixtures of Mallows models with Spearman distance is developed by relying on a twofold data augmentation strategy aimed at i) enlarging the applicability of Mallows models to samples drawn from heterogeneous populations, ii) dealing with partial rankings affected by diverse forms of censoring. Additionally, a novel approximation of the model normalizing constant is introduced to support the challenging model-based clustering of rankings with a large number of items. Extensive simulation studies assess the EM scheme's inferential ability and the approximation's effectiveness. Finally, we show that the application to three real-world datasets endorses our proposals also in comparison with competing mixtures of ranking models.