Learning Mixtures of Random Utility Models with Features from Incomplete Preferences

TL;DR

This paper extends mixtures of Random Utility Models with features to handle incomplete preferences, proves their identifiability, and demonstrates the effectiveness of maximum likelihood estimation through theoretical analysis and experiments.

Contribution

It generalizes RUMs with features to incomplete preferences, establishes conditions for identifiability, and analyzes the statistical and computational properties of MLE.

Findings

MLE is consistent for identifiable PL with features

Sample complexity bounds are derived for parameter estimation

Experiments show PL with features has strong predictive power

Abstract

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.