[Lecture] Kai Zhang：BEAUTY Powered BEAST
Time: 10:00-11:00am, Oct. 29th, 2021, Friday
Venue: ZOOM（ID：83654741182；password：631014）
Spreker: Kai Zhang, Associate Professor, The University of North Carolina, at Chapel Hill
Abstract:We study nonparametric dependence detection with the proposed binary expansion approximation of uniformity (BEAUTY) approach, which generalizes the celebrated Euler's formula, and approximates the characteristic function of any copula with a linear combination of expectations of binary interactions from marginal binary expansions. This novel theory enables a unification of many important tests through approximations from some quadratic forms of symmetry statistics, where the deterministic weight matrix characterizes the power properties of each test. To achieve a robust power, we study test statistics with data-adaptive weights, referred to as the binary expansion adaptive symmetry test (BEAST). By utilizing the properties of the binary expansion filtration, we show that the Neyman-Pearson test of uniformity can be approximated by an oracle weighted sum of symmetry statistics. The BEAST with this oracle provides a benchmark of feasible power against any alternative by leading all existing tests with a substantial margin. To approach this oracle power, we develop the BEAST through a regularized resampling approximation of the oracle test. The BEAST improves the empirical power of many existing tests against a wide spectrum of common alternatives and provides clear interpretation of the form of dependency when significant. This is joint work with Zhigen Zhao and Wen Zhou.
Speaker’s Bio:Dr. Kai Zhang is currently an associate professor with tenure at the Department of Statistics and Operations Research, UNC Chapel Hill. Dr. Zhang obtained his bachelor’s degree from Peking University in 2003, his Ph.D. degree in mathematics from Temple University in 2007, and his Ph.D. degree in statistics from the Wharton School, University of Pennsylvania in 2012. His research interests include nonparametric statistics, high-dimensional statistics, and post-selection inference. His research is supported by four grants from the National Science Foundation of the United States.
