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Statistical Classification via Robust Hypothesis Testing

In this letter, we consider multiple statistical classification problem where a sequence of n independent and identically distributed observations, that are generated by one of M discrete sources, need to be classified. The source distributions are not known, however one has access to labeled training sequences, of length N , from each source. We consider the case where the unknown source distributions are estimated from the training sequences, then the estimates are used as nominal distributions in a robust hypothesis test. Specifically, we consider the robust DGL test due to Devroye et al. and provide non-asymptotic exponential bounds, that are functions of N{n, on the error probability of classification.