东南大学数学学院邀请专家申请表
报告人 | 单位 | 中南财经政法大学 | |
报告题目 | Deep Generative Learning with Theoretical Guarantee | ||
报告时间 | 10月22日周二 14：00-15：00 | 地点 | 东南大学数学学院 第一报告厅 |
邀请人 | 闫 亮 | ||
报告摘要 | Learning underlying distributions from samples is one of the fundamental tasks in machine learning and statistics. In this talk we will present a new framework to learn the underlying generative models via bring the strength of optimal transportation, density ratio estimation and deep neural networks. First, the deep generative learning tasks is reformulated as finding the optimal transportation map between a simple distribution and the underlying target. The optimal transport map is characterized by the Monge-Ampere equation, which is hard to solve due to the nonlinearity even if we know the target. The infinitesimal linearized version of Monge-Ampere equation goes back to the continuity equation, whose vector fields is determined via the density ratio of the solution of continuity equation and the underlying target. We solve the continuity equationby estimating the density ratio iteratively via some sampling methods to overcomethe difficulty of unknown target.We bound the error of the numerical scheme. Connections of proposed framework with GANs and VAEs are discussed.Numerical simulation shows the proposed framework is stable and comparable with state-of-the art methods. | ||
报告人简介 | 焦雨领，2014年毕业于武汉大学数学与统计学院, 现就职于中南财经政法大学统计与数学学院统计学系，文澜学者, 副教授。主要从事数据科学（机器学习、统计计算、高维统计推断、反问题等）方面研究。主持国家自然科学基金面上项目、青年项目、湖北省自然科学基金面上项目、统计与数据科学前沿理论及应用教育部重点实验室课题各一项。在包括Applied and Computational Harmonic Analysis, SIAM Journal on Numerical Analysis, SIAM Journal on Scientific Computing, Journal of Machine Learning, ICML, Inverse Problems, IEEE Transactions on Signal Processing, IEEE Transactions on Neural Networks and Learning Systems, IEEE Transactions on Geoscience and Remote Sensing等期刊和会议上发表30余篇论文 | ||
