Learned Interpolation for Better Streaming Quantiles with Worst Case Guarantees
Name
Schiefer-schiefer-SM-EECS-2022-thesis.pdf
Description
Thesis PDF
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2.59 MB
Format
Adobe PDF
Checksum (MD5)
38d7ed31a410c988a4bc223e36966a9c
Author(s)
Schiefer, Nicholas
Advisor(s)
Indyk, Piotr
Date Issued
September 2022
Publisher
Massachusetts Institute of Technology
Abstract
An ε-approximate quantile sketch over a stream of n inputs approximates the rank of any query point q—that is, the number of input points less than q—up to an additive error of εn, generally with some probability of at least 1−1/ poly(n), while consuming o(n) space. While the celebrated KLL sketch of Karnin, Lang, and Liberty achieves a provably optimal quantile approximation algorithm over worst-case streams, the approximations it achieves in practice are often far from optimal. Indeed, the most commonly used technique in practice is Dunning’s t-digest, which often achieves much better approximations than KLL on real-world data but is known to have arbitrarily large errors in the worst case. We apply interpolation techniques to the streaming quantiles problem to attempt to achieve better approximations on real-world data sets than KLL while maintaining similar guarantees in the worst case.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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