Preference-based Teaching of Unions of Geometric Objects
Abstract
This paper studies exact learning of unions of non-discretized geometric concepts in the model of preference-based teaching. In particular, it focuses on upper and lower bounds of the corresponding sample complexity parameter, the preference-based teaching dimension (PBTD), when learning disjoint unions of a bounded number of geometric concepts of various types -- for instance balls, axis-aligned cubes, or axis-aligned boxes -- in arbitrary dimensions. It is shown that the PBTD of disjoint unions of some such types of concepts grows linearly with the number of concepts in the union, independent of the dimensionality. Teaching the union of potentially overlapping objects turns out to be more involved and is hence considered here only for unions of up to two objects.