汇报（一）

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）：拉斯维加斯9888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/

汇报（二）

Title（标题）：Independent Component Analysis Involving Autocorrelated Sources with Application to Functional Magnetic Resonance Imaging

Speaker（汇报人）：Prof.Haipeng Shen,The University of North Carolina at Chapel Hill

Time（功夫）：2012年6月28日（周四）下午03:15-04:15

Place（地址）：拉斯维加斯9888新楼217教室

Abstract（提要）：Independent component analysis (ICA) is an effective data-driven method for blind source separation. It has been successfully applied to separate source signals of interest from their mixtures. Most existing ICA procedures are carried out by relying solely on the estimation of the marginal density functions. In many applications, correlation structures within each source also play an important role besides the marginal distributions. One important example is functional magnetic resonance imaging (fMRI) analysis where the brain-function-related signals are temporally correlated. I shall talk about a novel ICA approach that fully exploits the correlation structures within the source signals. Our methodology is described and implemented using spectral density functions under the Whittle likelihood framework. The performance of the proposed method will be illustrated through extensive simulation studies and real fMRI application. The numerical results indicate that our approach outperforms several popular methods including the most widely used fastICA algorithm.

http://www.unc.edu/~haipeng/