I am currently a Research Fellow in the Dept. of Statistics at the University of Michigan, Ann Arbor, working with Prof. My research interest is high-dimensional analysis using stochastic processes, Makov chains, and time series with the Hidden Markov models (HMMs), which are a class of machine learning models that can be used to describe the evolution of observable events that depend on internal factors, which are not directly observable. They are of widespread importance throughout science and engineering, whose applications include ecology, economics, epidemiology, finance, meteorology, neuroscience, and target tracking, to name a few. In discrete time and continuous states HMMs, I co-developed the multivariate Bayesian structure time series model which is a machine learning model with feature selection for dimension reduction; I independently developed the multivariate quantile Bayesian structure time series model for multivariate quantile time series forecast with feature selection for dimension reduction; I am co-tackling the curse of dimension problem with the general nonlinear and non-Gaussian HMM, using the network language with techniques borrowed from statistics physics. In continuous time and continuous states HMMs which include stochastic volatility models, I co-established the well-posedness of high-dimensional stochastic volatility models with multivariate reflection boundaries, the asymptotic analysis of the super-hedging valuation problem driven by the uncertain stochastic volatility model in stochastic control, and the linkage between forward-backward hierarchical stochastic volatility styled stochastic differential equation with the viscosity solution of a quasilinear parabolic partial differential equation. My research areas include Applied Probability, Statistics, and Network; Stochastic Game, Stochastic Control and Optimization; Math Finance and Math Economics; Machine Learning, Artificial Intelligence, and Data Science. I serve as invited reviewers for Journal of Machine Learning Research, Annals of Applied Probability, Papers in Regional Science, Physical Review E, European Journal of Operation Research, IEEE Transactions on Engineering Management. |