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Random Utility Models (RUMs), which subsume Plackett-Luce model (PL) as aspecial case, are among the most popular models for preference learning. Inthis paper, we consider RUMs with features and their mixtures, where eachalternative has a vector of features, possibly different across agents. Suchmodels significantly generalize the standard PL and RUMs, but are not as wellinvestigated in the literature. We extend mixtures of RUMs with features tomodels that generate incomplete preferences and characterize theiridentifiability. For PL, we prove that when PL with features is identifiable,its MLE is consistent with a strictly concave objective function under mildassumptions, by characterizing a bound on root-mean-square-error (RMSE), whichnaturally leads to a sample complexity bound. We also characterizeidentifiability of more general RUMs with features and propose a generalizedRBCML to learn them. Our experiments on synthetic data demonstrate theeffectiveness of MLE on PL with features with tradeoffs between statisticalefficiency and computational efficiency. Our experiments on real-world datashow the prediction power of PL with features and its mixtures.

Learning Mixtures of Random Utility Models with Features from Incomplete Preferences