Interactive and nonparametric modeling of preferences on an ordinal scale using small data

Abstract

In this study, we consider learning preference structure of a Decision Maker (DM). Many preference modeling problems in a variety of fields such as marketing, quality control and economics involve possibly interacting criteria, and an ordinal scale is used to express preference of objects. In these cases, typically underlying preference structure of the DM and distribution of criteria values are not known, and only a few data can be collected about the preferences of the DM.For developing a preference model under such circumstances, we propose using nonparametric Statistical Learning approaches interactively. In particular, we employ Active Learning by asking a preference question to the DM at each step and try to reach a close approximation to the correct model in a small number of steps. Our experimental analysis proves that the proposed approach outperforms a “naive” approach where subsequent questions are asked randomly. In the study, we also provide algorithmic recommendations for modeling different underlying value functions, if information is available about the form of the preference structure and/or distribution of criteria values.This study can be regarded as a pioneering approach considering that Statistical Learning based approaches in the literature have been developed and tested based on a relatively large preference information and they do not interact with the DM in model developing process while Multi Criteria Decision Aid based approaches typically ignore interactions among the criteria, suffer from generalization ability, and have no concern about predicting equally good everywhere in the criteria domain.