Learning decision trees using the Fourier spectrum
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
A technique for upper bounding the spectral norm with applications to learning
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
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In many recent results in learning and computational complexity theory which rely on Fourier analysis, the spectral norm plays a key role. An understanding of this quantity would appear to be useful in both gauging and exploiting these results, and in understanding the underlying techniques. This paper surveys various aspects of the spectral norm of finite functions. We consider some of the motivating results as well as both upper and lower bounds on the spectral norm and their relationships to the computational complexity of the function. Some of the results included here are new. In particular, we introduce a general technique for upper bounding the spectral norm of a decision tree over an arbitrary basis. We also extend the learning algorithm of Kushilevitz and Mansour [KM] to mutually independent distributions.