Estimation of Markov Chain via Rank-constrained Likelihood

发布者:闻天明发布时间:2019-06-10浏览次数:13

Speaker:    Prof. Xudong Li

Time:        10:00-11:00, June 13

Location:    SIST 1C-201

Host:       Prof. Ziyu Shao

Abstract:

In this talk, we study the recovery and state compression of low-rank Markov chains from empirical trajectories. We propose a non-convex estimator based on rank-constrained likelihood maximization. Statistical upper bounds are provided for the Kullback-Leiber divergence and the l2 risk between the estimator and the true transition matrix. The estimator reveals a compressed state space of the Markov chain. We also develop a novel DC (difference of convex function) programming algorithm to tackle the rank-constrained non- smooth optimization problem. Convergence results are established. Experiments with taxi trip data show that the estimator is able to identify the zoning of Manhattan city.

Bio:

Xudong Li is a tenure-track associate professor at the School of Data Science, Fudan University. He is also affiliated with the Shanghai Center for Mathematical Sciences. His research focuses on the mathematical foundation of data science with emphasis on efficient algorithms for large-scale problems arising from operations research, machine learning and statistical estimations. He received his Ph.D.in Mathematics from National University of Singapore in 2015. From 2015 to 2017, he was a research fellow in the Department of Mathematics at National University of Singapore. Prior to joining FDU in Autumn 2018, he was a postdoctoral scholar in the Department of Operations Research and Financial Engineering at Princeton University.

SIST-Seminar 18174