主 题: Nonlinear Time Series Models via Hessian Regularization
报告人: Prof.Xiaoming Huo (霍晓明) (Georgia Institute of Technology Atlanta GA USA)
时 间: 2008-11-12 下午 4:00 - 5:00
地 点: 理科一号楼 1418
I will introduce a nonparametric nonlinear time series model. The key idea is to fit a model via penalization, where the penalty term is an unbiased estimator of the integrated hessian of the underlying function. Such a Hessian based penalty term is novel. The underlying model assumption is very general: it has hessian everywhere (or almost everywhere) in its domain. numerical experiments demonstrate that our model has better predictive power: if the underlying model complies with an
existing parametric/semiparametric form (e.g., a threshold autoregressive model (TAR), an additive autoregressive model (AAR), or a functional coefficient autoregressive model (FAR)), our model performs comparably; if the underlying model does not comply with any pre‐\existing form, our model performs better in near all simulations. We name our model a hessian regularized nonlinear model for time series (HRM). We conjecture on theoretical properties and use simulations to back up. We discuss
the feasibility of fast computing: our method can be as fast as fitting a smoothing spline in one dimension. Our approach can be viewed as a way to generalize splines to high dimensions (when the number of variates is more than three), under which an analogous analytical derivation cannot work due to the curse of dimensionality..
Bio:
Professor Huo received a B.S. degree in mathematics from the University of Science and Technology, Heifei, China, in 1993 and the M.S. degree in electrical engineering and the Ph.D. degree in statistics from Stanford University, Stanford, CA, in 1997 and 1999, respectively. He is an Associate Professor with
the School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta. His research interests include dimension reduction and nonlinear methods. Dr. Huo represented China and received first prize in the Thirtieth International Mathematical Olympiad (IMO), which was held in Braunschweig,
Germany, in 1989. He is an IEEE senior member, won Georgia Tech Sigma Xi Young Faculty Award in 2005, and was interviewed by Emerging Research Fronts (
http://www.esi‐\topics.com/erf/2006/june06‐\Donoho_Huo.html).
