Spectral Norm in Learning Theory: Some Selected Topics
Proceedings of ALT 2006
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.