Conditional independence relations and log-linear models for random permutations

TL;DR

This paper introduces a new class of log-linear models for random permutations, focusing on Luce-decomposable distributions and their conditional independence properties, with methods for parameter estimation and model testing.

Contribution

It develops a novel framework linking log-linear models to permutation distributions and provides algorithms for maximum likelihood estimation and conditional independence testing.

Findings

Characterization of Luce-decomposable permutation models

Development of an iterative maximum likelihood estimation algorithm

Ability to test data conformity to conditional independence relations

Abstract

We propose a new class of models for random permutations, which we call log-linear models, by the analogy with log-linear models used in the analysis of contingency tables. As a special case, we study the family of all Luce-decomposable distributions, and the family of those random permutations, for which the distribution of both the permutation and its inverse is Luce-decomposable. We show that these latter models can be described by conditional independence relations. We calculate the number of free parameters in these models, and describe an iterative algorithm for maximum likelihood estimation, which enables us to test if a set of data satisfies the conditional independence relations or not.