Title（标题）：A new approach of functional estimation for high-dimensional inputs

Speaker（汇报人）：Prof.Xiaoming Huo，The Georgia Institute of Technology

Time（功夫）：2012年6月28日（周四）下午02:00-03:00

Place（地址）：J9集团国际站新楼217教室

Abstract（提要）：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.

http://www2.isye.gatech.edu/~xiaoming/