Learning various classes of models of lexicographic orderings
Richard Booth, Yann Chevaleyre, Jérôme Lang, Jérôme Mengin, Chattrakul Sombattheera · Base Institutionnelle de Recherche de l'université Paris-Dauphine (BIRD) (University Paris-Dauphine) · 2009
We consider the problem of learning a user’s ordinal preferences onmultiattribute domains, assuming that the user’s preferences may be modelled asa kind of lexicographic ordering. We introduce a general graphical representationcalled LP-structures which captures various natural classes of such ordering inwhich both the order of importance between attributes and the local preferencesover each attributemay or may not be conditional on the values of other attributes.For each class we determine the Vapnik-Chernovenkis dimension, the communication complexity of learning preferences, and the complexity of identifying amodel in the class consistent with some given user-provided examples.