Spectral Norm in Learning Theory: Some Selected Topics

Author: Hans Ulrich Simon

Source: Algorithmic Learning Theory, 17th International Conference, ALT 2006, Barcelona, October 2006, Proceedings, (José L. Balcázar, Phil Long and Frank Stephan, Eds.), Lecture Notes in Artificial Intelligence 4264, pp. 13 - 27, Springer 2006.

Abstract. In this paper, we review some known results that relate the statistical query complexity of a concept class to the spectral norm of its correlation matrix. Since spectral norms are widely used in various other areas, we are then able to put statistical query complexity in a broader context. We briefly describe some non-trivial connections to (seemingly) different topics in learning theory, complexity theory, and cryptography. A connection to the so-called Hidden Number Problem, which plays an important role for proving bit-security of cryptographic functions, will be discussed in somewhat more detail.

This work was supported in part by the IST Programme of the European Community, under the PASCAL Network of Excellence, IST-2002-506778. This publication only reflects the authors' views.

©Copyright 2006, Springer