Consistent Weighted Sampling

We describe an ecient procedure for sampling representa- tives from a weighted set such that the probability that for any weightings S and T, the probability that the two choose the same sample is the Jacard similarity: Pr(sample(S) = sample(T)) = P x min(S(x),T(x)) P x max(S(x),T(x)) . The sampling process takes expected time linear in the num- ber of non-zero weights, independent of the weights them- selves. We discuss and develop the implementation of our sam- pling schemes, reducing the requisite computation substan- tially, and reducing the randomness required to only four bits in expectation.