Learning How to Teach or Selecting Minimal Surface Data

Learning a map from an input set to an output set is similar to the problem of reconstructing 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 and the one oflearning how to teach. Our key step is to introduce a process that statistically selects the data according to the model. During the process of data selection (learning how to teach) our system (teacher) is capable of predicting the new surface, the approximated one provided by the selected data.