We propose an EM-based framework for learning PlackettLuce model and its mixtures from partial orders. The core of our framework is the efficient sampling of linear extensions of partial orders under Plackett-Luce model. We propose two Markov Chain Monte Carlo (MCMC) samplers: Gibbs sampler and the generalized repeated insertion method tuned by MCMC (GRIM-MCMC), and prove the efficiency of GRIM-MCMC for a large class of preferences. Experiments on synthetic data show that the algorithm with Gibbs sampler outperforms that with GRIM-MCMC. Experiments on real-world data show that the likelihood of test dataset increases when (i) partial orders provide more information; or (ii) the number of components in mixtures of PlackettLuce model increases.
In particular, Liu et al. REF proposed an EM-based algorithm to learn from general partial orders.
Learning Plackett-Luce Mixtures from Partial Preferences
AAAI
Computer Science