Source distinguishability under corrupted training

We study a new variant of the source identification game with training data in which part of the training data is corrupted by an adversary. In such a scenario, the defender wants to decide whether a test sequence x(n) has been drawn from the same source which generated a training sequence t(N), part of which has been corrupted by the adversary. By adopting a game theoretical formulation, we derive the unique rationalizable equilibrium of the game in the asymptotic setup. Moreover, by mimicking Stein's lemma, we derive the best achievable performance for the defender, permitting us to analyze the ultimate distinguishability of the two sources. We conclude the paper by comparing the performance of the test with corrupted training to the simpler case in which the adversary can not modify the training sequence, and by deriving the percentage of samples that the adversary needs to modify to make source identification impossible.