Inference Algorithms for the Multiplicative Mixture Mallows Model

A popular approach to obtain a consensus ranking from ranking data is based on the probabilistic, distance-based Mallows model comprising of a modal permutation and dispersion parameters. Often, the population consists of several subpopulations. As a result, finite mixture models are used to distinguish latent sub-groups of individuals in a heterogeneous population. Given a finite number of subpopulations each based on the Mallows model, a popular inference approach is the computationally intensive expectation maximization algorithm for additive models. We address the drawbacks of this model using a novel multiplicative mixture Mallows model (M4). Given complete ranking observations from a heterogeneous population, we derive inference algorithms for the joint estimation of the parameters and the consensus rankings of the component distributions. We numerically validate the permutation estimation performance of the proposed algorithms on synthetic datasets. We also demonstrate the goodness-of-fit using the Bayesian information criterion and the integrated complete likelihood on the real-world APA and Sushi datasets.