The informational complexity of learning from examples

This thesis attempts to quantify the amount of information needed to learn certain tasks. The tasks chosen vary from learning functions in a Sobolev space using radial basis function networks to learning grammars in the principles and parameters framework of modern linguistic theory. These problems are analyzed from the perspective of computational learning theory and certain unifying perspectives emerge. Copyright c Massachusetts Institute of Technology, 1996 This report describes research done within the Center for Biological and Computational Learning in the Department of Brain and Cognitive Sciences and at the Arti cial Intelligence Laboratory at the Massachusetts Institute of Technology. This research is sponsored by a grant from the National Science Foundation under contract ASC-9217041 (this award includes funds from ARPA provided under the HPCC program); and by a grant from ARPA/ONR under contract N00014-92-J-1879. Additional support has been provided by Siemens Corporate Research Inc., Mitsubishi Electric Corporation and Sumitomo Metal Industries. Support for the A.I. Laboratory's arti cial intelligence research is provided by ARPA contract N00014-91-J-4038. The Informational Complexity of Learning from