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学术报告

Efficient algorithms for large-scale optimal transport problems

孟澄   助理教授

（中国人民大学）

报告时间： 2022年11月2日 (星期三) 上午10：30-11：30

腾讯会议 ID： 865-197-122   报告地点 ： 沙河主楼E404

报告摘要：Wasserstein distance is a popular metric to quantify the discrepancy between two probability measures. Recently, Wasserstein distance has played an increasingly predominant role in machine learning, statistics, computer vision, and biomedical research. Despite the wide application, existing methods for calculating the Wasserstein distance may suffer from a substantial computational burden when the sample size is large. We introduce two methodologies to alleviate the computational burden. One is called the Hilbert curve projection distance, which utilizes the Hilbert space-filling curve to construct an effective surrogate of the Wasserstein distance. The other approach is called Spar-Sink, which utilizes a novel importance sparsification scheme to accelerate the popular Sinkhorn algorithm. This approach can be effectively applied in the entropic optimal transport problem, unbalanced optimal transport problem, and Gromov-Wasserstein distance approximation. Numerical studies on various synthetic and real-world datasets demonstrate the superior performance of the proposed methods in comparison with mainstream competitors, requiring significantly less computational time.

报告人简介：孟澄，中国人民大学统计与大数据研究院助理教授。2015年毕业于清华大学数学系获学士学位，2020年毕业于美国佐治亚大学获统计学博士学位。主要研究方向为大数据子抽样，最优输运问题，非参数统计等。论文主要发表在Biometrika，JCGS，NeurIPS等统计与机器学习期刊会议。2021年获国家自然科学基金青年项目资助。

邀请人： 夏勇