Permutation Complexity Bound on Out-Sample Error

Part of Advances in Neural Information Processing Systems 23 (NIPS 2010)

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Malik Magdon-Ismail


We define a data dependent permutation complexity for a hypothesis set \math{\hset}, which is similar to a Rademacher complexity or maximum discrepancy. The permutation complexity is based like the maximum discrepancy on (dependent) sampling. We prove a uniform bound on the generalization error, as well as a concentration result which means that the permutation estimate can be efficiently estimated.