时 间：2025年10月29日 15:00 -16:00
地 点：普陀校区理科大楼A1514
报告人：骆威 浙江大学研究员（预聘副教授）
主持人：马慧娟 华东师范大学副教授
摘 要：
Fitting a Gaussian Mixture Model (GMM) is commonly recognized to be computationally challenging, especially when the data are large dimensional. In this paper, we propose a new type of unsupervised dimension reduction technique to extract the essential part of the data that preserves the mixing pattern in GMM, which facilitates the implementation by fitting GMM on the reduced data only. This technique can also be applied to more general clustering analysis and other supervised learning problems centered on detecting non-Gaussian signals. We build the general theory of the new type of dimension reduction, such as defining the identifiable parameterization and elaborating the singularity assumptions, with special attention to GMM. Inspired by Stein's lemma, we propose the first family of dimension reduction methods that are applicable in high-dimensional settings, and, with the aid of data augmentation technique, we propose the second and more general family of methods in connection to the literature of supervised sufficient dimension reduction. These methods are computationally efficient, and their effectiveness in the scenario of GMM is illustrated in the numerical studies at the end.
报告人简介：
骆威于2014年毕业于美国宾夕法尼亚州立大学，之后任职于美国Baruch College,于2018年加入浙江大学。骆威的研究方向包括充分降维和因果推断，在Annals of Statistics, Biometrika, JRSSB, JMLR等统计和机器学习国际学术期刊上发表了多篇论文，目前主持国家青年科学基金项目（B类）。