SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Optimal sampling from sliding windows
Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Functional Monitoring without Monotonicity
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
A near-optimal algorithm for estimating the entropy of a stream
ACM Transactions on Algorithms (TALG)
Proceedings of the forty-second ACM symposium on Theory of computing
1-pass relative-error Lp-sampling with applications
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
On the exact space complexity of sketching and streaming small norms
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Proceedings of the forty-third annual ACM symposium on Theory of computing
Near-optimal private approximation protocols via a black box transformation
Proceedings of the forty-third annual ACM symposium on Theory of computing
Fast moment estimation in data streams in optimal space
Proceedings of the forty-third annual ACM symposium on Theory of computing
Continuous distributed monitoring: a short survey
Proceedings of the First International Workshop on Algorithms and Models for Distributed Event Processing
Wiki-Watchdog: Anomaly Detection in Wikipedia Through a Distributional Lens
WI-IAT '11 Proceedings of the 2011 IEEE/WIC/ACM International Conferences on Web Intelligence and Intelligent Agent Technology - Volume 01
Optimal sampling from sliding windows
Journal of Computer and System Sciences
Space-efficient estimation of statistics over sub-sampled streams
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Tight bounds for distributed functional monitoring
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Synopses for Massive Data: Samples, Histograms, Wavelets, Sketches
Foundations and Trends in Databases
Tracking distributed aggregates over time-based sliding windows
SSDBM'12 Proceedings of the 24th international conference on Scientific and Statistical Database Management
The continuous distributed monitoring model
ACM SIGMOD Record
Fast approximation of matrix coherence and statistical leverage
The Journal of Machine Learning Research
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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 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.