Multi-Attribute Preferences: A Transfer Learning Approach

TL;DR

This paper presents a transfer learning method based on Bradley-Terry models to improve estimation of primary attribute preferences by leveraging secondary attribute data, with theoretical guarantees and practical application.

Contribution

It introduces a novel transfer learning approach for pairwise comparison models that enhances primary attribute estimation using secondary data, including a data-driven method for selecting informative attributes.

Findings

Improved estimation rates for primary attribute preferences.

The method outperforms traditional Bradley-Terry models in simulations.

Application to consumer preference data demonstrates practical utility.

Abstract

This contribution introduces a novel statistical learning methodology based on the Bradley-Terry method for pairwise comparisons, where the novelty arises from the method's capacity to estimate the worth of objects for a primary attribute by incorporating data of secondary attributes. These attributes are properties on which objects are evaluated in a pairwise fashion by individuals. By assuming that the main interest of practitioners lies in the primary attribute, and the secondary attributes only serve to improve estimation of the parameters underlying the primary attribute, this paper utilises the well-known transfer learning framework. To wit, the proposed method first estimates a biased worth vector using data pertaining to both the primary attribute and the set of informative secondary attributes, which is followed by a debiasing step based on a penalised likelihood of the primary attribute. When the set of informative secondary attributes is unknown, we allow for their estimation by a data-driven algorithm. Theoretically, we show that, under mild conditions, the $\ell_\infty$ and $\ell_2$ rates are improved compared to fitting a Bradley-Terry model on just the data pertaining to the primary attribute. The favourable (comparative) performance under more general settings is shown by means of a simulation study. To illustrate the usage and interpretation of the method, an application of the proposed method is provided on consumer preference data pertaining to a cassava derived food product: eba. An R package containing the proposed methodology can be found on https://CRAN.R-project.org/package=BTTL.