The remarkable empirical performance of Generative Adversarial Networks (GANs) in generating high-quality samples have attracted enormous attention in the past few years. In this talk, we discuss how well can GANs approximate and learn high-dimensional distributions. We show that deep ReLU neural networks can transform a low-dimensional source distribution to a distribution that is arbitrarily close to a high-dimensional target distribution in Wasserstein distance. The approximation order only depends on the intrinsic dimension of the target distribution. While only finite samples are observed, we prove that GANs are consistent estimators of the data distributions under Wasserstein distance, if the generator and discriminator network architectures are properly chosen. Furthermore, the convergence rates do not depend on the high ambient dimension, but on the lower intrinsic dimension of target distribution, which implies GANs can overcome the curse of dimensionality.

4月21日
10:00am - 11:00am
地點
https://hkust.zoom.us/j/5906683526 (Passcode: 5956)
講者/表演者
Mr. Yunfei YANG
主辦單位
Department of Mathematics
聯絡方法
付款詳情
對象
Alumni, Faculty and staff, PG students, UG students
語言
英語
其他活動
3月24日
研討會, 演講, 講座
IAS / School of Science Joint Lecture - Pushing the Limit of Nonlinear Vibrational Spectroscopy for Molecular Surfaces/Interfaces Studies
Abstract Surfaces and interfaces are ubiquitous in Nature. Sum-frequency generation vibrational spectroscopy (SFG-VS) is a powerful surface/interface selective and sub-monolayer sensitive spect...
11月22日
研討會, 演講, 講座
IAS / School of Science Joint Lecture - Leveraging Protein Dynamics Memory with Machine Learning to Advance Drug Design: From Antibiotics to Targeted Protein Degradation
Abstract Protein dynamics are fundamental to protein function and encode complex biomolecular mechanisms. Although Markov state models have made it possible to capture long-timescale protein co...