Mallows Ranking Models: Maximum Likelihood Estimate and Regeneration

Abstract

This paper is concerned with various Mallows ranking models. We study the statistical properties of the MLE of Mallows' φ 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.

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