Learning How to Teach or Selecting Minimal Surface Data

Marques Pereira Dipartimento di Informatica Universita di Trento Via Inama 7, Trento, TN 38100 ITALY Abstract Learning a map from an input set to an output set is similar to the problem ofreconstructing hypersurfaces from sparse data (Poggio and Girosi, 1990). In this framework, we discuss the problem of automatically selecting "minimal"surface data. The objective is to be able to approximately reconstruct the surface from the selected sparse data. We show that this problem is equivalent to the one of compressing information by data removal andthe one oflearning how to teach. Our key step is to introduce a process that statistically selects the data according to the model.