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As increasing amounts of sensitive personal information is aggregated into data repositories, it has become important to develop mechanisms for processing the data without revealing information about individual data instances. The differential privacy model provides a framework for the development and theoretical analysis of such mechanisms. In this paper, we propose an algorithm for learning a discriminatively trained multiclass Gaussian mixture model-based classifier that preserves differential privacy using a large margin loss function with a perturbed regularization term. We present a theoretical upper bound on the excess risk of the classifier introduced by the perturbation.