We outline an empirical permutation procedure
used to estimate classification accuracy when
there are very few samples, this type of procedure
is used in a variety of scientific applications.
It effectively balances approximation and timation
errors to ensure that the size of the hypothesis space is appropriate. We give rates for the concentration of the permutation procedure.
Approximation and estimation bounds will also be given for the problem of estimating a density using a finite combination of densities from a given class. The bound on the estimation error decreases as the number of densities in the
finite combination increases.
The first part is joint work with Pollina Golland and Dmitry Panchenko The scond part was joint work with Alex Rakhlin and Dmitry Panchenko
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