In consumer theory, ranking available objects by means of preference relations yields the most common description of individual choices. However, preference-based models assume that individuals: (1) give their preferences only between pairs of objects; (2) are always able to pick the best preferred object. In many situations, they may be instead choosing out of a set with more than two elements and, because of lack of information and/or incomparability (objects with contradictory characteristics), they may not able to select a single most preferred object. To address these situations, we need a choice-model which allows an individual to express a set-valued choice. Choice functions provide such a mathematical framework. We propose a Gaussian Process model to learn choice functions from choice-data. The proposed model assumes a multiple utility representation of a choice function based on the concept of Pareto rationalization, and derives a strategy to learn both the number and the values of these latent multiple utilities. Simulation experiments demonstrate that the proposed model outperforms the state-of-the-art methods.

翻译：在消费者理论中，通过偏好关系对可用对象进行排序是描述个体选择的最常见方式。然而，基于偏好的模型假设个体：(1) 仅能给出对象对之间的偏好；(2) 始终能够选出最偏好的对象。但在许多情境下，个体可能需从多于两个元素组成的集合中进行选择，并且由于信息缺失和/或不可比性（对象具有矛盾特征），可能无法选出唯一最优对象。为应对这些情况，我们需要一种允许个体表达集合值选择的选择模型。选择函数为此提供了数学框架。我们提出一种高斯过程模型，用于从选择数据中学习选择函数。该模型基于帕累托合理化概念，假设选择函数具有多重效用表示，并推导出同时学习这些潜在多重效用的数量与值的策略。仿真实验表明，所提模型优于现有最先进方法。