Learned Interpolation for Better Streaming Quantile Approximation with Worst-Case Guarantees
This work addresses the gap between theoretical optimality and practical performance in streaming quantile approximation, which is incremental as it builds on existing methods like KLL and t-digest.
The paper tackles the problem of improving quantile approximation accuracy on real-world data streams while maintaining worst-case guarantees, by applying interpolation techniques to achieve better practical performance than the KLL sketch.
An $\varepsilon$-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 $\varepsilon n$, generally with some probability of at least $1 - 1/\mathrm{poly}(n)$, 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.