A new approach of functional estimation for high-dimensional inputs
Education 1993.7, BS Mathematics, University of Science and Technology of China 1996.4, MS Statistics, Stanford University 1997.4, MS EE, Stanford University 1999.9, PhD Statistics, Stanford University Award/Honor Before College: 1989, Gold prize in the 30th International Mathematical Olympiad (IMO) held in Braunschweig, Germany. Before College: Ranked No.2 in China's national mathematical competition - selected for that year's IMO participation. Undergraduate: Zhang-Zong-Zhi Fellowship, Hua-Wei Fellowship, etc... IEEE senior member, May 2004. Fellow, IPAM, Sep. 2004. Georgia Tech Sigma Xi Young Faculty Award 2005. An interview with Emerging Research Fronts, June 2006
Functional estimation with low input dimension is a well solved problem. When the dimension of the input goes up, the geometry of the functional domain becomes more delicate in several ways: the intrinsic dimension of the domain could be lower than its apparent dimension; the domain could take irregular shapes--in particular, could not be approximated by hyper-rectangles. A straightforward adaptation of penalization approach will result in non-optimal performance. We proposed a data-driven method, which provably achieves the best possible known minimax rate under the framework of nonparametric functional estimation. The essence of the new approach is to utilize the Taylor expansions at all observational points to estimate the functional values, and an innovative way to fuse them together. Numerical experiments will be presented to illustrate its performance in finite sample cases.