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Profile Entropy: A Fundamental Measure for the Learnability and Compressibility of Distributions
Yi Hao · Alon Orlitsky

Wed Dec 09 09:00 PM -- 11:00 PM (PST) @ Poster Session 4 #1190

The profile of a sample is the multiset of its symbol frequencies. We show that for samples of discrete distributions, profile entropy is a fundamental measure unifying the concepts of estimation, inference, and compression. Specifically, profile entropy: a) determines the speed of estimating the distribution relative to the best natural estimator; b) characterizes the rate of inferring all symmetric properties compared with the best estimator over any label-invariant distribution collection; c) serves as the limit of profile compression, for which we derive optimal near-linear-time block and sequential algorithms. To further our understanding of profile entropy, we investigate its attributes, provide algorithms for approximating its value, and determine its magnitude for numerous structural distribution families.

Author Information

Yi Hao (University of California, San Diego)

Fifth-year Ph.D. student supervised by Prof. Alon Orlitsky at UC San Diego. Broadly interested in Machine Learning, Learning Theory, Algorithm Design, Symbolic and Numerical Optimization. Seeking a summer 2020 internship in Data Science and Machine Learning.

Alon Orlitsky (University of California, San Diego)

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