Poster
Estimation of Entropy in Constant Space with Improved Sample Complexity
Maryam Aliakbarpour · Andrew McGregor · Jelani Nelson · Erik Waingarten
Hall J (level 1) #819
Keywords: [ Sample Complexity ] [ Shannon Entropy ] [ Data streams ]
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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