  Random Utility Models (RUMs), which subsume Plackett-Luce model (PL) as a
special case, are among the most popular models for preference learning. In
this paper, we consider RUMs with features and their mixtures, where each
alternative has a vector of features, possibly different across agents. Such
models significantly generalize the standard PL and RUMs, but are not as well
investigated in the literature. We extend mixtures of RUMs with features to
models that generate incomplete preferences and characterize their
identifiability. For PL, we prove that when PL with features is identifiable,
its MLE is consistent with a strictly concave objective function under mild
assumptions, by characterizing a bound on root-mean-square-error (RMSE), which
naturally leads to a sample complexity bound. We also characterize
identifiability of more general RUMs with features and propose a generalized
RBCML to learn them. Our experiments on synthetic data demonstrate the
effectiveness of MLE on PL with features with tradeoffs between statistical
efficiency and computational efficiency. Our experiments on real-world data
show the prediction power of PL with features and its mixtures.
