Recursive inversion models for permutations

We develop a new exponential family model for permutations that can capture hierarchical structure in preferences, and that has the well known Mallows models as a subclass. The Recursive Inversions Model (RIM), unlike most distributions over permutations of n items, has a flexible structure, represented by a binary tree. We describe how to compute marginals in the RIM, including the partition function, in closed form. Further we introduce methods for the Maximum Likelihood estimation of parameters and structure search for this model. We demonstrate that this added flexibility both improves predictive performance and enables a deeper understanding of collections of permutations.