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arXiv · 2610.08134

Almost Instance Optimal Sum and Moment Estimation Using Weighted Sampling

Anup Bhattacharya·Suryendu Mondal·Pinki Pradhan
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Abstract

We design an almost instance optimal algorithm for the sum estimation problem using weighted sampling. We show that the sample complexity for sum estimation is closely related to the $\ell_2$ norm of the weighted sampling distribution. We show an almost instance optimal lower bound for this problem as well. We also study the moment estimation problem and design an algorithm that has better instance-wise sample complexity bounds.

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Anup Bhattacharya, Suryendu Mondal, Pinki Pradhan. 2026-10-06. Almost Instance Optimal Sum and Moment Estimation Using Weighted Sampling. https://arxiv.org/abs/2610.08134

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