  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.
