Entrywise Error Analysis and Uncertainty Quantification in Heterogeneous Preference Learning from Revealed Choice Behavior

Music City Center 

This paper studies human preference learning based on partially revealed choice behavior. We formulate the problem as a generalized Bradley–Terry–Luce (BTL) ranking model that accounts for heterogeneous preferences. Specifically, we assume that each user is associated with a nonparametric preference function, and each item is characterized by a low-dimensional latent feature vector — their interaction defines the underlying score matrix.

In this formulation, we propose an indirect regularization method for collaboratively learning the score matrix, which ensures entrywise error control — a novel contribution to the heterogeneous preference learning literature. This technique is based on sieve approximation and can be extended to a broader class of binary response models where a smooth link function is adopted. In addition, by applying a single step of the Newton–Raphson method, we debias the regularized estimator and establish uncertainty quantification for item scores and rankings, both for the aggregated and individual preferences. Extensive simulation results from synthetic and real datasets corroborate our theoretical findings.