Sampling and Learning Mallows and Generalized Mallows Models Under the Cayley Distance

The Mallows and Generalized Mallows models are compact yet powerful and natural ways of representing a probability distribution over the space of permutations. In this paper, we deal with the problems of sampling and learning such distributions when the metric on permutations is the Cayley distance. We propose new methods for both operations, and their performance is shown through several experiments. An application in the field of biology is given to motivate the interest of this model.