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arXiv · 2506.07342

On Sketching Trimmed Statistics

Honghao Lin·Hoai-An Nguyen·David P. Woodruff
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Abstract

We study sketching trimmed statistics of a frequency vector, including the $F_p$ moment of the top-$k$ coordinates and of the trimmed-$k$ vector. Despite their natural role in robust analytics, this is the first time these problems have been studied in any sublinear space setting. For $p \in [0,2]$, we obtain $poly(\log n/\varepsilon)$-space algorithms for both tasks when $k$ is moderately large, and for general $k$ we identify a sharp structural threshold that characterizes exactly when sublinear space is possible: in particular, it is actually determined by the ratio between $a_k^2$ and $\|x_{-k}\|_2^2/k$. We extend these results to $p > 2$ and present several applications including algorithms for thresholded $F_p$ estimation and generalized impact indices. Notably, we improve the space bounds of Govindan, Monemizadeh, and Muthukrishnan (PODS 2017) for computing the $h$-index.

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Honghao Lin, Hoai-An Nguyen, David P. Woodruff. 2025-06-09. On Sketching Trimmed Statistics. https://arxiv.org/abs/2506.07342

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