A Bayesian Mallows Approach to Non-Transitive Pair Comparison Data: How Human Are Sounds?

• Activity Number: 404 - Bayesian Clustering and Classification
• Type: Contributed
• Date/Time: Tuesday, August 1, 2017 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Marta Crispino* and Natasha Barrett and Arnoldo Frigessi and Elja Arjas and Valeria Vitelli
• Companies: Bocconi University and Norges musikkhøgskole and OCBE, UiO and University of Helsinki, & OCBE, UiO and University of Oslo
• Keywords: Pairwise comparisons ; non-transitivity ; ranking data ; Mallows model ; Bayesian learning ; mixture model

Abstract

We propose a Bayesian probabilistic method to learn preferences from non-transitive pairwise comparison data, as happens for example when item A is preferred to item B, B to C, and then C to A, the opposite of what expected. Lack of transitivity arises when the items compared are perceived as rather similar and when the pairwise comparisons are presented sequentially without allowing for consistency checks. We build an extension of the Bayesian Mallows model of Vitelli et al., 2017, in order to handle non-transitive data, by adding a latent layer of uncertainty which captures the generation of preference misreporting. We then develop a mixture extension of the Mallows model, able to learn individual preferences of a heterogeneous population, which is particularly important in applications. We are interested in learning how listeners perceive sounds as having human origins. An experiment was performed with a series of electronically synthesized sounds, and listeners were asked to compare them in pairs. The result of our analysis is particularly relevant for composers and sound designers whose aim is to understand how computer generated sounds can be sound more human.