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- W4288409568 abstract "A $t$-digest is a compact data structure that allows estimates of quantiles which increased accuracy near $q = 0$ or $q=1$. This is done by clustering samples from $mathbb R$ subject to a constraint that the number of points associated with any particular centroid is constrained so that the so-called $k$-size of the centroid is always $le 1$. The $k$-size is defined using a scale function that maps quantile $q$ to index $k$. Since the centroids are real numbers, they can be ordered and thus the quantile range of a centroid can be mapped into an interval in $k$ whose size is the $k$-size of that centroid. The accuracy of quantile estimates made using a $t$-digest depends on the invariance of this constraint even as new data is added or $t$-digests are merged. This paper provides proofs of this invariance for four practically important scale functions." @default.
- W4288409568 created "2022-07-29" @default.
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- W4288409568 date "2019-03-24" @default.
- W4288409568 modified "2023-10-16" @default.
- W4288409568 title "Conservation of the $t$-digest Scale Invariant" @default.
- W4288409568 doi "https://doi.org/10.48550/arxiv.1903.09919" @default.
- W4288409568 hasPublicationYear "2019" @default.
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