主 题: Latent Graphical Model for Mixed Data
报告人: Jianqing Fan (Princeton University)
时 间: 2014-06-19 14:00-15:00
地 点: 光华老楼111教室（统计中心活动）
Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete variables or a combination of both continuous and discrete variables poses new challenges in statistical modeling. In this paper, we propose a semiparametric model named latent Gaussian copula model for binary and mixed data. The observed binary data are assumed to be obtained by dichotomizing a latent variable satisfying the Gaussian copula distribution or the nonparanormal distribution. The latent Gaussian model with the assumption that the latent variables are multivariate Gaussian is a special case of the proposed model. A novel rank-based approach is proposed for both latent graph estimation and latent principal component analysis. Theoretically, the proposed methods achieve the same rates of convergence for both precision matrix estimation and eigenvector estimation, as if the latent variables were observed. Under similar conditions, the consistency of graph structure recovery and feature selection for leading eigenvectors is established. The performance of the proposed methods is numerically assessed through simulation studies, and the usage of our methods is illustrated by a genetic dataset.
About the speaker
Jianqing Fan is Frederick L. Moore Professor of Finance, Professor of Statistics, Chairman of Department of Operations Research and Financial Engineering, and Director of Committee of Statistical Studies, Princeton University, where he directs both financial econometrics and statistics labs. He was the past president of the Institute of Mathematical Statistics and International Chinese Statistical Association, and was an invited speaker at the 2006 International Congress of Mathematicians. He is co-editing Journal of Econometrics and is an and Journal of American Statistical Association, and was the co-editor of The Annals of Statistics, Probability Theory and Related Fields and Econometrics Journal. After receiving his Ph.D. from the University of California at Berkeley in 1989, he has been appointed as assistant, associate, and full professor at the University of North Carolina at Chapel Hill (1989-2003), professor at the University of California at Los Angeles (1997-2000), Professor and Chairman at Chinese University of Hong Kong (2000-2003), and professor at Princeton University (2003--). His published work on statistics, computational biology, and finance has been recognized by the 2000 COPSS Presidents' Award, the Myrto Lefkopoulou distinguished lecture of Harvard School of Public Health, the 2007 Morningside Gold Medal of Applied Mathematics, Guggenheim Fellow in 2009, and election to Academician of Academia Sinica and follow of American Associations for Advancement of Science, Institute of Mathematical Statistics, and American Statistical Association.