Taylor Polynomial Estimator for Estimating Frequency Moments

We present a randomized algorithm for estimating the pth moment Fp of the frequency vector of a data stream in the general update (turnstile) model to within a multiplicative factor of 1±ǫ, for p > 2, with high constant confidence. For 0 < ǫ ≤ 1, the algorithm uses space O(nǫ+ nǫ log(n)) words. This improves over the current bound of O(nǫ log(n)) words by Andoni et. al. in [2]. Our space upper bound matches the lower bound of Li and Woodruff [23] for ǫ = (log(n)) and the lower bound of Andoni et. al. [3] for ǫ = Ω(1).