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SURF: A Simple, Universal, Robust, Fast Distribution Learning Algorithm
Yi Hao · Ayush Jain · Alon Orlitsky · Vaishakh Ravindrakumar

Wed Dec 09 09:00 PM -- 11:00 PM (PST) @ Poster Session 4 #1257
Sample- and computationally-efficient distribution estimation is a fundamental tenet in statistics and machine learning. We present $\SURF$, an algorithm for approximating distributions by piecewise polynomials. $\SURF$ is: simple, replacing prior complex optimization techniques by straight-forward empirical probability approximation of each potential polynomial piece through simple empirical-probability interpolation, and using plain divide-and-conquer to merge the pieces; universal, as well-known polynomial-approximation results imply that it accurately approximates a large class of common distributions; robust to distribution mis-specification as for any degree $d \le 8$, it estimates any distribution to an $\ell_1$ distance $< 3$ times that of the nearest degree-$d$ piecewise polynomial, improving known factor upper bounds of 3 for single polynomials and 15 for polynomials with arbitrarily many pieces; fast, using optimal sample complexity, running in near sample-linear time, and if given sorted samples it may be parallelized to run in sub-linear time. In experiments, $\SURF$ outperforms state-of-the art algorithms.

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.

Ayush Jain (UC San Diego)
Alon Orlitsky (University of California, San Diego)
Vaishakh Ravindrakumar (UC San Diego)

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