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Pattern recognition problems involving learning with a bad teacher or learning without a teacher require the updating of the conditional densities of unknown parameters using a mixture of probability density functions. Mixtures of density functions in general are not reproducing and hence the computations are infeasible. For learning without a teacher, a computationally feasible scheme has been suggested by Agrawala . The learning procedure proposed by Agrawala makes use of a probabilistic labeling scheme. The probabilistic labeling scheme is extended to allow the use of reproducing densities for a large class of problems, including the problem of learning with an imperfect teacher.