摘要: Variable selection plays an important role in data mining for high-dimensional nonlinear systems. However, the current variable selection methods are either developed for linear systems or computationally infeasible, rendering imprecise selection of relevant variables. In general, variable selection for high-dimensional nonlinear systems suffers from three difficulties: (i) an unknown functional form of the nonlinear system, (ii) model consistency, and (iii) highly-demanding computation. To circumvent the first difficulty, we employ a feed-forward neural network to approximate the unknown nonlinear function motivated by its universal approximation ability. To circumvent the second difficulty, we conduct structure selection for the neural network, which induced variable selection, by choosing appropriate prior distributions that lead to consistency in variable selection. To circumvent the third difficulty, we implement the population stochastic approximation Monte Carlo algorithm, a parallel adaptive Markov Chain Monte Carlo algorithm, on the OpenMP platform which provides a linear speedup for simulations. The numerical results indicate that the proposed method can execute very fast on multicore computers and work very well for identification of relevant variables for general high-dimensional nonlinear systems. The proposed method is successfully applied to personalized medicine and selection of anticancer drug response genes for the cancer cell line encyclopedia (CCLE) data.

个人简介：

Faming Liang, PhD, is Preeminent Professor, University of Florida, USA. Dr. Liang is an ASA fellow, IMS fellow, and an Elected Member of ISI. Dr. Liang has served as associate editor for a number of journals, such as Journal of the American Statistical Association, Biometrics, Technometrics, Journal of Computational and Graphical Statistics, Bayesian Analysis, and Annals of Mathematical Sciences and Applications. Dr. Liang graduated from Chinese University of Hong Kong in 1997 under the advisor of Professor Wing Hung Wong. After graduation, he took a short stay in UCLA and National University of Singapore, and then joined Texas A&M University in 2002, where his career grew from Assistant Professor to Full Professor. In 2014, he joined University of Florida in his current position. Dr. Liang has wide research interests including Markov chain Monte Carlo, spatial statistics, bioinformatics, machining learning, and big data. Dr. Liang has published two books and authored over 100 papers, and many of his papers have appeared in top-tier statistical journals.