PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Sparse classification boundaries
Yu. Ingster, C. Pouet and A.B. Tsybakov
(2009) arxiv paper.


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.

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Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
ID Code:6922
Deposited By:Alexandre Tsybakov
Deposited On:16 April 2010