Speaker: Aaditya Ramdas (Carnegie Mellon University)
"Uniform, nonparametric, non-asymptotic confidence sequences"
11 December 2018, 12:30PM
Bocconi University, Room 3.b3.sr01
via Roentgen 1, 3rd floor
A confidence sequence is a sequence of confidence intervals that is uniformly valid over an unbounded time horizon. In this paper, we develop non-asymptotic confidence sequences under nonparametric conditions that achieve arbitrary precision. Our technique draws a connection between the classical Cramer-Chernoff method, the law of the iterated logarithm (LIL), and the sequential probability ratio test (SPRT) — our confidence sequences extend the first to produce time-uniform concentration bounds, provide tight non-asymptotic characterizations of the second, and generalize the third to nonparametric settings, including sub-Gaussian and Bernstein conditions, self-normalized processes, and matrix martin- gales. We strengthen and generalize existing constructions of finite-time iterated logarithm (“finite LIL”) bounds. We illustrate the generality of our proof techniques by deriving an empirical-Bernstein finite LIL bound as well as a novel upper LIL bound for the maximum eigenvalue of a sum of random matrices. Finally, we demonstrate the utility of our approach with applications to covariance matrix estimation and to estimation of sample average treatment effect under the Neyman-Rubin potential outcomes model, for which we give a non-asymptotic, sequential estimation strategy which handles adaptive treatment mechanisms such as Efron’s biased coin design.
Aaditya Ramdas is an assistant professor in the Department of Statistics and Data Science and the Machine Learning Department at Carnegie Mellon University. Previously, he was a postdoctoral researcher in Statistics and EECS at UC Berkeley from 2015-18, mentored by Michael Jordan and Martin Wainwright. He finished his PhD at CMU in Statistics and Machine Learning, advised by Larry Wasserman and Aarti Singh, winning the Best Thesis Award. A lot of his research focuses on modern aspects of reproducibility in science and technology — involving statistical testing and false discovery rate control in static and dynamic settings. He also works on some problems in sequential decision-making and online uncertainty quantification.