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 Xác suất - Thống kê tháng 07/2022 với báo cáo sau:
- Tên bài báo cáo: Adaptive variational Bayes: Optimality, computation and applications
- Báo cáo viên: PGS. TS Lizhen Lin (Department of Applied and Computational Mathematics and Statistics, The University of Notre Dame)
- Thời gian: 9g30 thứ năm 28/07/2022
- Địa điểm: Phòng F207, Đại học Khoa học Tự nhiên, 227 Nguyễn Văn Cừ, Q. 5, TP. HCM
- Tóm tắt: In this talk, we discuss adaptive statistical inference based on variational Bayes. Although a number of studies have been conducted to analyze theoretical properties such as posterior contraction properties of variational posteriors, there is still a lack of general and computationally tractable variational Bayes methods that can achieve adaptivity and optimal contraction of the variational posterior. We propose a novel and general variational Bayes framework, called adaptive variational Bayes, which can operate on a collection of models with varying dimensions and structures. The proposed framework combines variational posteriors over individual models with certain weights to obtain a variational posterior over the entire model. It turns out that this combined variational posterior minimizes the Kullback-Leibler divergence to the original posterior distribution. We show that the proposed variational posterior achieves optimal contraction rates adaptively under very general conditions and attains model selection consistency when the true model structure exists. We apply the general results obtained for the adaptive variational Bayes to a large class of statistical models including deep learning models and derive some new and adaptive inference results. We consider applications of this adaptive variational bayes framework to various numerical examples including examples on finite mixture modeling and deep neural network models.