报告时间：12月25日周一下午 13:30-14:30
报告地点：法商南楼135会议室
报告人： Jianguo Liu, Duke University
报告题目：Some mathematical questions in deep learning
报告摘要：In this talk I will present some mathematical questions in deep learning including:
(1) Rigorous justification of the small jump approximation of the stochastic gradient descent (SGD) and online principal component analysis (PCA).
SGD and its variants are the most common tools in the supervised learning and it is widely believed that the behavior of SGDs shall be described by stochastic differential equations (SDE). I will present a simple and rigorous justification of this claim by using small jump approximation theory in Markov process. This is a joint work with Lei Li (Duke) and Yuanyuan Feng (CMU)
(2) Shape estimates on the escape time for SGD to escape from unstable stationary points including both saddle points and local maximums. This is a central question in deep learning in very high dimensional and non-convex statistical optimization. I will present a result on shape rate escape time using the theory of large deviation of random dynamical system. This is a joint work with Lei Li (Duke) and Junchi Li (Princeton)
(3) Online learning in optical tomography by stochastic gradient descent (SGD)
Many of inverse problems can be formatted as statistics optimization problems and online deep learning methods such as SGD can be used to effectively solve the prohibitive memory and computation problem in very high dimensions. I will present a successful example of online learning in optical tomography which has many applications in medial image. This is a joint work with Ke Chen and Qin Li (U Wisconsin-Madison).
(4) A modified Levy jump-diffusion model based on market sentiment memory for online jump prediction.
Data assimilation contribute greatly to the success of wealth predication and it is realized by the observation data for many local stations. The idea can be extended to jump diffusion model for option pricing. I will present a method using the market sentiment data collected from Internet to model the Levy jump diffusion model for option pricing. This is a joint work with Lei Li (Duke) and Bill Zhu (Stanford)
报告人简介：Jianguo Liu教授1982年毕业于复旦大学数学系，博士毕业于加州大学洛杉矶分校，现任Duke University物理系和数学系双聘教授。Jianguo Liu教授在应用数学，数值分析等领域学术造诣极高，目前已发表100多篇文章。Jianguo Liu教授在深度学习领域也颇有研究心得，本次报告将为大家介绍深度学习中的若干数学问题。
报告时间：12月25日周一下午 14:30-15:30
报告地点：法商南楼135会议室
报告人： Yanyuan Ma, 宾夕法尼亚州立大学
报告题目：On Estimation of General Index Model for Survival Data
报告摘要：We propose a general index model for survival data, which generalizes many commonly used semi parametric survival models and belongs to the framework of dimension reduction. Using a combination of geometric approach in semiparametric and martingale treatment in survival data analysis, we devise estimation procedures that are feasible and do not require covariate-independent censoring as assumed in many dimension reduction methods for censored survival data. We establish the root-n consistency and asymptotic normality of the proposed estimators and derive the most efficient estimator in this class for the general index model. Numerical experiments are carried out to demonstrate the empirical performance of the proposed estimators and an application to an AIDS data further illustrates the usefulness of the work.
报告人简介：马彦源教授博士毕业于麻省理工学院，现任职于宾夕法尼亚州立大学统计系，马教授主要研究领域有降维、测量误差、半参数模型等，已在统计学四大国际顶级期刊Annals of Statistics, JASA, JRSSB, Biometrika上发表30余篇文章