Sketching and Streaming Entropy via Approximation Theory

@article{Harvey2008SketchingAS,
  title={Sketching and Streaming Entropy via Approximation Theory},
  author={Nicholas J. A. Harvey and Jelani Nelson and Krzysztof Onak},
  journal={2008 49th Annual IEEE Symposium on Foundations of Computer Science},
  year={2008},
  pages={489-498}
}
We give near-optimal sketching and streaming algorithms for estimating Shannon entropy in the most general streaming model, with arbitrary insertions and deletions. This improves on prior results that obtain suboptimal space bounds in the general model, and near-optimal bounds in the insertion-only model without sketching. Our high-level approach is simple: we give algorithms to estimate Tsallis entropy, and use them to extrapolate an estimate of Shannon entropy. The accuracy of our estimates… CONTINUE READING
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