Bộ môn Xác suất - Thống kê kính mời quý thầy cô, nghiên cứu sinh, học viên cao học và các sinh viên có quan tâm đến tham dự Seminar Thống kê và Khoa học dữ liệu tháng 07/2023 với báo cáo sau: 

  • Tên bài báo cáo: Statistical foundations of deep generative models 
  • Báo cáo viên: GS. Lizhen Lin (Department of Mathematics, University of Maryland, College Park)
  • Thời gian: 9g30 thứ năm 27/07/2023
  • Địa điểm: Phòng E202B, Trường Đại học Khoa học Tự nhiên, 227 Nguyễn Văn Cừ, Q. 5, TP. HCM
  • Tóm tắt: Deep generative models are probabilistic generative models where the generator is parameterized by a deep neural network. They are popular models for modeling high-dimensional data such as texts, images and speeches, and have achieved impressive empirical success. Despite demonstrated success in  empirical performance,  theoretical understanding of such models  is largely lacking . We investigate statistical properties of deep generative models from a nonparametric distribution estimation viewpoint. In the considered model, data are assumed to be observed in some high-dimensional ambient space but concentrate around some low-dimensional structure such as a lower-dimensional manifold. Estimating the distribution supported on this low-dimensional structure is challenging due to its singularity with respect to the Lebesgue measure in the ambient space. We obtain convergence rates with respect to the Wasserstein metric of  distribution estimators based on two methods: a sieve MLE based on the perturbed data and a GAN type estimator. Such an analysis  provides  insights into  i) how deep generative models can avoid the curse of dimensionality and outperform classical nonparametric estimates,  and  ii) how likelihood approaches work for singular distribution estimation, especially in adapting to the intrinsic geometry of the data.