The Statistics Seminar kicks off the Fall 2018 semester on Wednesday, September 19, with Jayadev Acharya, an assistant professor in school of ECE, Cornell University, where he joined after a postdoc at MIT. He holds a Ph.D. from UC San Diego. His research interests are in algorithms, information theory, machine learning, and statistics. His received a Jack Wolf Student paper award at ISIT'10, and a Best Paper Honorable Mention at ICML'17 (which is the primary work this talk is based on).
Talk: Estimating Symmetric Properties of Distributions: Maximum Likelihood Strikes Back!
Abstract: Symmetric distribution properties such as support size, support coverage, entropy, and proximity to uniformity, arise in many applications. Specialized estimators and analysis tools were recently used to derive sample-optimal estimators for each of these properties. We show that a single, simple, plug-in estimator—profile maximum likelihood (PML)—is sample competitive for all symmetric properties, and in particular is asymptotically sample-optimal for all the properties above.
Our technical results include: - A bound on the performance of general Maximum Likelihood Estimation as a function of the underlying domain size. - Improved estimators for various symmetric properties with sharp phase transitions in the error probability.
Our results on symmetric properties follow from combining these with Hardy-Ramanujan's bounds on partition numbers. We will conclude with a number of open directions, both computational and statistical.
Joint work with Hirakendu Das, Alon Orlitsky, and Ananda Theertha Suresh.
Refreshments will be served following the seminar in 1181 Comstock Hall.