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arXiv · 2205.09804

Estimation of Entropy in Constant Space with Improved Sample Complexity

Maryam Aliakbarpour·Andrew McGregor·Jelani Nelson·Erik Waingarten
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Abstract

Recent work of Acharya et al. (NeurIPS 2019) showed how to estimate the entropy of a distribution $\mathcal D$ over an alphabet of size $k$ up to $\pm\epsilon$ additive error by streaming over $(k/\epsilon^3) \cdot \text{polylog}(1/\epsilon)$ i.i.d. samples and using only $O(1)$ words of memory. In this work, we give a new constant memory scheme that reduces the sample complexity to $(k/\epsilon^2)\cdot \text{polylog}(1/\epsilon)$. We conjecture that this is optimal up to $\text{polylog}(1/\epsilon)$ factors.

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Maryam Aliakbarpour, Andrew McGregor, Jelani Nelson, Erik Waingarten. 2022-05-19. Estimation of Entropy in Constant Space with Improved Sample Complexity. https://arxiv.org/abs/2205.09804

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