Geometry of Data

Schedule

Day Title / Notes Reading Homework
Tu 8/23 Introduction    
Th 8/25 Intro, cont.   HW 1, Due Tu 9/13
Tu 8/30 Topology Basics Riemannian Geometry Notes (Section 1)  
Th 9/1 Topology Basics, cont.    
Tu 9/6 Manifold Basics RGN (Section 2)  
Th 9/8 Manifold Basics, cont.    
Tu 9/13 Tom out sick! – No Class   HW 1 Due
Th 9/15 Tangent Spaces    
Tu 9/20 Riemannian Geometry RGN (Section 3) HW 2, Due Th 10/13
Th 9/22 Riemannian Geometry, cont.    
Tu 9/27 Introduction to Shape Manifolds: Kendall’s Shape Space Kendall, 1984  
Th 9/29 Statistics on Manifolds: Frechet Mean Pennec, 1999  
Tu 10/4 Reading Day – No Class    
Th 10/6 Statistics on Manifolds: Principal Geodesic Analysis Fletcher 2019, Section 3  
Tu 10/11 Introduction to Manifold Learning:
Multidimensional Scaling
Cayton, 2005  
Th 10/13 MDS cont., Isomap Tenenbaum, de Silva, Langford, 2000 HW 2 Due
Tu 10/18 Local Linear Embedding, Laplacian Eigenmaps Roweis & Saul, 2000
Belkin & Niyogi, 2003
 
Th 10/20 Manifold geometry of neural networks Goodfellow et al. 2016, Chapter 14  
Tu 10/25 Neural networks, cont.    
Th 10/27 Variational Autoenconders (VAEs) Kingma and Welling, 2014 HW 3, Due Mo 11/28
notebook and data
Tu 11/1 Lie groups RGN (Section 4)  
Th 11/3 Lie algebras, Lie group actions RGN (Section 5.1)
Parallel parking and Lie brackets
 
Tu 11/8 Election Day – No Class    
Th 11/10 Lie exponential and log maps Applications of Lie groups:
Simard, et al. 1998
Casado and Rubio, 2019
 
Tu 11/15 Class canceled    
Th 11/17 Fisher information metric and Gaussians Fisher Information
Fisher Information Metric
 
Tu 11/22 Natural gradients Pascanu and Bengio, 2014
Score-based Generative Models
HW 4, Due Th 12/8
Th 11/24 Thanksgiving – No Class    
Tu 11/29 Information theory basics, entropy    
Th 12/1 Kullback-Leibler divergence    
Tu 12/6 Hamiltonian Monte Carlo Neal, 2011
Ghahramani, 2016 (slides)
Saatchi and Wilson, 2017