Permutation Complexity Bound on Out-Sample Error

We define a data dependent permutation complexity for a hypothesis set H, which is similar to a Rademacher complexity or maximum discrepancy. The crucial difference is that it is based on permutation (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.

Permutation Complexity Bound on Out-Sample Error

We define a data dependent permutation complexity for a hypothesis set H, 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.