讲座题目: Continuous Normalizing Flows for Learning Probability Distributions

主讲人：黄坚 教授（香港理工大学）

讲座时间：2024年12月8日上午9:00-9:50

讲座地点：深圳大学粤海校区校友广场303会议室

报告内容：Continuous normalizing flows (CNFs) are a generative method based on ordinary differential equations for learning probability distributions. This method has shown success in applications like image synthesis, protein structure prediction, and molecule generation. We present the CNF method and study its theoretical properties using a flow matching objective function. We establish non-asymptotic error bounds for the distribution estimator based on CNFs, in terms of the Wasserstein-2 distance, under the assumption that the target distribution has bounded support, is strongly log-concave, or is a mixture of Gaussian distributions. Our convergence analysis addresses errors due to velocity estimation, discretization, and early stopping. We also develop uniform error bounds with Lipschitz regularity control for deep ReLU networks approximating the Lipschitz function class. Our analysis provides theoretical guarantees for using CNFs to learn probability distributions from finite random samples.报告人简历：Jian Huang is a Chair Professor of Data Science and Analytics in the Departments of Data Science and AI, and Applied Mathematics at The Hong Kong Polytechnic University. He earned his Ph.D. in Statistics from the University of Washington in Seattle. His current research interests include machine learning, deep generative models, representation learning, large model statistics, and AI for science. He has published extensively in the fields of Statistics, Biostatistics, Machine Learning, Bioinformatics, and Econometrics. He was designated a Highly Cited Researcher in the field of Mathematics by Clarivate from 2015 to 2019. He was also included in the list of the top 2% of the world's most cited scientists by Stanford University from 2019 to 2024. He serves on the editorial boards of the Journal of the American Statistical Association and the Journal of the Royal Statistical Society (Series B). Professor Huang is a Fellow of the American Statistical Association and a Fellow of the Institute of Mathematical Statistics.

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邀请人：数学科学学院（周彦）

                                       数学科学学院

                                2024年12月5日