DATE2021-11-25 15:10-16:00

PLACE化學館 36104教室

SPEAKER楊鈞澔 助理教授(國立台灣大學數學系

TITLEGeometry, Statistics, and Deep Learnin

ABSTRACT There will be two parts in this seminar talk: (1) the application of geometry in statistics and deep learning and (2) the problem of dimension reduction for data on a Grassmann manifold. In the first part, I will briefly introduce some research areas where geometry meets statistics and deep learning. There are two main directions: (i) studying the geometry of statistical models (information geometry) and (ii) statistical analysis of geometric data (geometric statistics and geometric deep learning). I will also point out some interesting research problems in these areas. In the second part, I will discuss a research problem that I have been working on recently: dimension reduction with nested Grassmann manifolds. In this work, we proposed to use the nested structure of Grassmann manifolds to solve the dimension reduction problem for data residing on a Grassmann manifold. The main application is in dimension reduction of planar shapes.