Abstract
Regression using pairwise comparison data between given instances but without using their objective values is called “uncoupled regression.” In this study, we propose its extension to Gaussian process regression. For example, when developing a new product specification, more preferred by customers, based on customer questionnaire results on many ready-made products, we do not expect that the customers can evaluate their preferences by setting numeric scores consistent across the customers. This is due to the variety of individual customers’ value scales. On the other hand, the collection of the evaluations mutually consistent among the customers is easier, if we apply pairwise comparison based questionnaires regarding the preference of products A or B. While a previous study has proposed an uncoupled regression method that enables point estimation of the objective value for each instance, we propose a Gaussian process based uncoupled regression method, which can evaluate the uncertainty of the regression model and its objective values. We show that the accuracy of the proposed method is practical in comparison with the supervised kernel ridge regression results through numerical experiments. This enables wider application of uncoupled regression, such as the design and development of efficient product specifications that take into account the uncertainty of estimated preference.
