The Complexity of Approximating the Entropy

We consider the problem of approximating the entropy of a discrete distribution under several different models of oracle access to the distribution. In the evaluation oracle model, the algorithm is given access to the explicit array of probabilities specifying the distribution. In this model, linear time in the size of the domain is both necessary and sufficient for approximating the entropy. In the generation oracle model, the algorithm has access only to independent samples from the distribution. In this case, we show that a γ-multiplicative approximation to the entropy can be obtained in O (