WOR and p's: Sketches for ℓ_p-Sampling Without Replacement [article]

Edith Cohen, Rasmus Pagh, David P. Woodruff
2020 arXiv   pre-print
Weighted sampling is a fundamental tool in data analysis and machine learning pipelines. Samples are used for efficient estimation of statistics or as sparse representations of the data. When weight distributions are skewed, as is often the case in practice, without-replacement (WOR) sampling is much more effective than with-replacement (WR) sampling: it provides a broader representation and higher accuracy for the same number of samples. We design novel composable sketches for WOR ℓ_p
more » ... weighted sampling of keys according to a power p∈[0,2] of their frequency (or for signed data, sum of updates). Our sketches have size that grows only linearly with the sample size. Our design is simple and practical, despite intricate analysis, and based on off-the-shelf use of widely implemented heavy hitters sketches such as CountSketch. Our method is the first to provide WOR sampling in the important regime of p>1 and the first to handle signed updates for p>0.
arXiv:2007.06744v3 fatcat:sns6m6vyabbcfjqqwarvnjifzm