Sparse classification boundaries
Yu. Ingster, C. Pouet and A.B. Tsybakov
Given a training sample of size m from a d-dimensional population, we
wish to allocate a new observation Z to this population or to the noise.
We suppose that the difference between the distribution of the population
and that of the noise is only in a shift, which is a sparse vector. For the Gaussian
noise, fixed sample size m, and the dimension d that tends to infinity, we
obtain the sharp classification boundary and we propose classifiers attaining
this boundary. We also give extensions of this result to the case where the
sample size m depends on d and to the case of non-Gaussian noise satisfying the Cramer condition.