We study the sublinear mean estimation problem. Specifically, we aim to output a point minimizing the sum of squared Euclidean distances. We show that a multiplicative (1+ε) approximation can be found with probability 1-δ using O(ε⁻¹log δ⁻¹) many independent random samples. We also provide a matching lower bound.
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Bertolotti et al. (2024) studied this question.
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