报告人：高俊斌 教授 (悉尼大学)

报告题目：Coupling Matrix Manifolds and Their Applications in Optimal Transport

报告人简介：Junbin Gao is Professor of Big Data Analytics at the University of Sydney Business School. Prior to joining the University of Sydney in 2016, he was Professor in Computing from 2010 to 2016 and Associate Professor from 2005 to 2010 at Charles Sturt University (CSU). He was Senior Lecturer from Jan 2005 to July 2005 and Lecturer from Nov 2001 to Jan 2005 in the School of Mathematics, Statistics and Computer Science (now the School of Science and Technology) at University of New England (UNE). Between 1999 and 2001, he worked as a Research Fellow in the Department of Electronics and Computer Science at University of Southampton, England. Until recently his major research interest has been machine learning and its application in data science, image analysis, pattern recognition, Bayesian learning & inference, and numerical optimization etc. He is the author of 360 academic research papers and two books. His recent research has involved new machine learning algorithms for big data in business. Prof Gao won two research grants in Discovery Project theme from the prestigious Australian Research Council (ARC).

报告摘要: Optimal transport (OT) is a powerful tool for measuring the distance between two defined probability distributions. In this research, we develop a new manifold named the coupling matrix manifold (CMM), where each point on CMM can be regarded as the transportation plan of the OT problem.

We firstly explore the Riemannian geometry of CMM with the metric expressed by the Fisher information. These geometrical features of CMM have paved the way for developing numerical Riemannian optimization algorithms such as Riemannian gradient descent and Riemannian trust region algorithms, forming a uniform optimization method for all types of OT problems. The proposed method is then applied to solve several OT problems studied by previous literature. The results of the numerical experiments illustrate that the optimization algorithms that are based on the method proposed in this paper are comparable to the classic ones, for example the Sinkhorn algorithm, while outperforming other state-of-the-art algorithms without considering the geometry information, especially in the case of non-entropy optimal transport.

报告时间: 2019年10月28日（星期一）上午10：00-12:00

报告地点: 科技楼南楼602室