Algorithms and Complexity Seminar

Sketching and Streaming Entropy via Approximation Theory

Jelani Nelson (MIT)

I will present near-optimal sketching and streaming algorithms for estimating Shannon entropy in the most general streaming model, with arbitrary insertions and deletions. This improves upon 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 Renyi and Tsallis entropy, and use them to extrapolate an estimate of Shannon entropy. The accuracy of our estimates is proven using approximation theory arguments and extremal properties of Chebyshev polynomials. Our work also yields the best-known and near-optimal additive approximations for entropy, and hence also for conditional entropy and mutual information.

This talk is based upon joint work with Nicholas J. A. Harvey (MSR / UWaterloo) and Krzysztof Onak (MIT) and will appear at FOCS 2008.