An optimal approximation of discrete random variables with respect to the Kolmogorov distance
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We present an algorithm that takes a discrete random variable X and a number m and computes a random variable whose support (set of possible outcomes) is of size at most m and whose Kolmogorov distance from X is minimal. In addition to a formal theoretical analysis of the correctness and of the computational complexity of the algorithm, we present a detailed empirical evaluation that shows how the proposed approach performs in practice in different applications and domains.
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