Permutation Models for Collaborative Ranking

We study the problem of collaborative filtering where ranking information is available. Focusing on the core of the collaborative ranking process, the user and their community, we propose new models for representation of the underlying permutations and prediction of ranks. The first approach is based on the assumption that the user makes successive choice of items in a stage-wise manner. In particular, we extend the Plackett-Luce model in two ways - introducing parameter factoring to account for user-specific contribution, and modelling the latent community in a generative setting. The second approach relies on log-linear parameterisation, which relaxes the discrete-choice assumption, but makes learning and inference much more involved. We propose MCMC-based learning and inference methods and derive linear-time prediction algorithms

Bayesian inference for bivariate ranks

A recommender system based on ranks is proposed, where an expert's ranking of a set of objects and a user's ranking of a subset of those objects are combined to make a prediction of the user's ranking of all objects. The rankings are assumed to be induced by latent continuous variables corresponding to the grades assigned by the expert and the user to the objects. The dependence between the expert and user grades is modelled by a copula in some parametric family. Given a prior distribution on the copula parameter, the user's complete ranking is predicted by the mode of the posterior predictive distribution of the user's complete ranking conditional on the expert's complete and the user's incomplete rankings. Various Markov chain Monte-Carlo algorithms are proposed to approximate the predictive distribution or only its mode. The predictive distribution can be obtained exactly for the Farlie-Gumbel-Morgenstern copula family, providing a benchmark for the approximation accuracy of the algorithms. The method is applied to the MovieLens 100k dataset with a Gaussian copula modelling dependence between the expert's and user's grades.Comment: 21 page