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Stream Sampling for Variance-optimal Estimation of Subset Sums by Cohen, Edith; Duffield, Nick; Kaplan, Haim; Lund, Carsten; Thorup, Mikkel is a scholarly article available to read on EtoBox.

What is Stream Sampling for Variance-optimal Estimation of Subset Sums about?

From a high volume stream of weighted items, we want to maintain a generic sample of a certain limited size $k$ that we can later use to estimate the total weight of arbitrary subsets. This is the classic context of on-line reservoir sampling, thinking of the generic sample as a reservoir. We present an efficient reservoir sampling scheme, $\varoptk$, that dominates all previous schemes in terms of estimation quality. $\varoptk$ provides {\em variance optimal unbiased estimation of subset sums}. More precisely, if we have seen $n$ items of the stream, then for {\em any} subset size $m$, our scheme based on $k$ samples minimizes the average variance over all subsets of size $m$. In fact, the optimality is against any off-line scheme with $k$ samples tailored for the concrete set of items seen. In addition to optimal average variance, our scheme provides tighter worst-case bounds on the variance of {\em particular} subsets than previously possible. It is efficient, handling each new item of the stream in $O(\log k)$ time. Finally, it is particularly well suited for combination of samples from different streams in a distributed setting.

Author

Cohen, Edith; Duffield, Nick; Kaplan, Haim; Lund, Carsten; Thorup, Mikkel

Published

2008

Language

EN