Learning Probabilistic CP-nets from Observations of Optimal Items

International audienceModelling preferences has been an active research topic in Artificial Intelligence for more than fifteen years. Existing formalisms are rich and flexible enough to describe the behaviour of complex decision rules. However, for being interesting in practice, these formalisms must also permit fast elicitation of a user's preferences, involving a reasonable amount of interaction only. Therefore, it is interesting to learn not a single model, but a probabilistic model that can compactly represent the preferences of a group of users - this model can then be finely tuned to fit one particular user. Even in contexts where a user is not anonymous, her preferences are usually ill-known, because they can depend on the value of non controllable state variable. In such contexts, we would like to be able to answer questions like "What is the probability that o is preferred to o' by some (unknown) agent?", or "Which item is most likely to be the preferred one, given some constraints?". We study in this paper how Probabilistic Conditional Preference networks can be learnt, both in off-line and on-line settings. We suppose that we have a list of items which, it is assumed, are or have been optimal for some user or in some context. Such a list can be, for instance, a list of items that have been sold. We prove that such information is sufficient to learn a partial order over the set of possible items, when these have a combinatorial structure