Learning Mixtures of Plackett-Luce Models with Features from Top-$l$ Orders

Plackett-Luce model (PL) is one of the most popular models for preference learning. In this paper, we consider PL with features and its mixture models, where each alternative has a vector of features, possibly different across agents. Such models significantly generalize the standard PL, but are not as well investigated in the literature. We extend mixtures of PLs with features to models that generate top-$l$ and characterize their identifiability. We further 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. Our experiments on synthetic data demonstrate the effectiveness of MLE on PL with features with tradeoffs between statistical efficiency and computational efficiency when $l$ takes different values. Our experiments on real-world data show the prediction power of PL with features and its mixtures.