🤖 AI Summary
This paper addresses the problem of learning individual heterogeneous preferences from partially observed choice behaviors. Conventional Bradley–Terry–Luce (BTL) models fail to capture preference heterogeneity and nonlinear user-item interactions. To overcome this, we propose a generalized BTL ranking model that represents users and items via low-dimensional latent features and models their interaction through a nonparametric preference function, yielding a score matrix. Methodologically, we design an indirect ℓ∞-regularization framework integrating sieve approximation, low-rank matrix estimation, and one-step Newton debiasing—enabling, for the first time, uncertainty quantification at both aggregate and individual ranking levels. We establish theoretical bounds on estimation error and empirically validate the method on synthetic and real-world datasets, demonstrating high-accuracy score prediction and reliable confidence assessment for rankings. The approach significantly enhances expressive power and statistical interpretability in preference modeling.
📝 Abstract
This paper studies human preference learning based on partially revealed choice behavior and formulates 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 low-rank score matrix. In this formulation, we propose an indirect regularization method for collaboratively learning the score matrix, which ensures entrywise $ell_infty$-norm 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 choice 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 of items, both for the aggregated and individual preferences. Extensive simulation results from synthetic and real datasets corroborate our theoretical findings.