A0894
Title: Entrywise error analysis and uncertainty quantification in heterogeneous preference learning from revealed choices
Authors: Jianqing Fan - Princeton University (United States)
Xiaonan Zhu - Princeton University (United States)
Hyukjun Kwon - Princeton University (United States) [presenting]
Abstract: The purpose is to study human preference learning based on partially revealed item comparisons. The problem is formulated as a generalized Bradley-Terry-Luce (BTL) ranking model that accounts for heterogeneous user preferences. Specifically, it is assumed that each user is associated with a nonparametric preference function, and each item is characterized by a low-dimensional latent feature vector; the interaction between them defines the underlying score matrix. Through regularization, the score matrix is collaboratively learned, and entrywise error control is established, representing a novel contribution to the heterogeneous preference learning literature. Notably, the analysis hinges on the innovative reparameterization of the regularized problem, which allows for leveraging a nonconvex surrogate problem for analyzing the original regularized formulation. 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, the regularized estimator is debiased, and uncertainty quantification is established for item scores and rankings, both for the aggregated and individual preferences. Extensive simulation results from synthetic and real datasets corroborate the theoretical findings.
