ncku-talk2021-11-25

Colloquium

DATE 2021-11-25　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）

TITLE Geometry, 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.

Colloquium

DATE	2021-11-25　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）

TITLE	Geometry, 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.