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# Mallows ranking models: maximum likelihood estimate and regeneration

*Proceedings of the 36th International Conference on Machine Learning*, PMLR 97:6125-6134, 2019.

#### Abstract

This paper is concerned with various Mallows ranking models. We study the statistical properties of the MLE of Mallows’ $\phi$ model. We also make connections of various Mallows ranking models, encompassing recent progress in mathematics. Motivated by the infinite top-$t$ ranking model, we propose an algorithm to select the model size $t$ automatically. The key idea relies on the renewal property of such an infinite random permutation. Our algorithm shows good performance on several data sets.