Asymptotic theory of finite dimensional normed spaces
Asymptotic theory of finite dimensional normed spaces
Estimating the Optimal Margins of Embeddings in Euclidean Half Spaces
COLT '01/EuroCOLT '01 Proceedings of the 14th Annual Conference on Computational Learning Theory and and 5th European Conference on Computational Learning Theory
Limitations of learning via embeddings in euclidean half spaces
The Journal of Machine Learning Research
Embedding with a Lipschitz function
Random Structures & Algorithms
Learning complexity vs communication complexity
Combinatorics, Probability and Computing
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We show that for any class of functions H which has a reasonable combinatorial dimension, the vast majority of small subsets of the combinatorial cube can not be represented as a Lipschitz image of a subset of H, unless the Lipschitz constant is very large. We apply this result to the case when H consists of linear functionals of norm at most one on a Hilbert space, and thus show that “most” classification problems can not be represented as a reasonable Lipschitz loss of a kernel class.