Hierarchical Sampling from Sketches: Estimating Functions over Data Streams

We present a randomized procedure named Hierarchical Sampling from Sketches ( Hss ) that can be used for estimating a class of functions over the frequency vector f of update streams of the form (𝒮)=∑_i=1^nψ(|f_i| ) . We illustrate this by applying the Hss technique to design nearly space-optimal algorithms for estimating the p th moment of the frequency vector, for real p ≥2 and for estimating the entropy of a data stream.