Geometry of Data

Schedule

Day Title / Notes Reading Homework
Tu 8/22 Introduction    
Th 8/24 Topology Basics Riemannian Geometry Notes (Section 1) HW 1, Due Tu 9/12
Tu 8/29 Topology Basics cont. Riemannian Geometry Notes (Section 1)  
Th 8/31 Manifold Basics RGN (Section 2)  
Tu 9/5 Manifold Basics cont. RGN (Section 2)  
Th 9/7 Tangent Spaces RGN (Section 2)  
Tu 9/12 Riemannian Geometry RGN (Section 3) HW 1 Due
Th 9/14 Riemannian Geometry, cont. RGN (Section 3) HW 2, Due Tu 10/10
Tu 9/19 Introduction to Shape Manifolds: Kendall’s Shape Space Kendall, 1984  
Th 9/21 Statistics on Manifolds: Frechet Mean Pennec, 1999  
Tu 9/26 Statistics on Manifolds: Principal Geodesic Analysis Fletcher 2019, Section 3  
Th 9/28 Introduction to Manifold Learning:
Multidimensional Scaling, Isomap
Cayton, 2005
Tenenbaum, de Silva, Langford, 2000
 
Tu 10/3 Reading Day – No Class    
Th 10/5 Manifold Learning:
Local Linear Embedding, Laplacian Eigenmaps
Roweis & Saul, 2000
Belkin & Niyogi, 2003
Project Proposal, Due Tu 10/24
Tu 10/10 Manifold geometry of neural networks
Recorded Lecture (no in-person class)
Goodfellow et al. 2016, Chapter 14 HW 2 Due
Th 10/12 Variational Autoenconders (VAEs)
Recorded Lecture (no in-person class)
Kingma and Welling, 2014  
Tu 10/17 Lie groups RGN (Section 4)  
Th 10/19 Lie algebras RGN (Section 5.1)
Parallel parking and Lie brackets
HW 3, Due Mon 11/6
notebook and data
Tu 10/24 Lie group actions Applications of Lie groups:
Simard, et al. 1998
Casado and Rubio, 2019
Project Proposal Due
Th 10/26 Flow based models Glow
RealNVP
 
Tu 10/31 Self-supervised Learning SimCLR  
Th 11/2 Image-Text Contrastive Learning CLIP  
Tu 11/7 Election Day – No Class    
Th 11/9 Unsupervised Learning + Fisher information metric and Gaussians Fisher Information
Fisher Information Metric
HW 4, Due Wed 11/22
Tu 11/14 Natural gradients Pascanu and Bengio, 2014
Score-based Generative Models
 
Th 11/16 Diffusion Models Denoising Diffusion Probabilistic Models  
Tu 11/21 Graph Neural Networks   Final Project, Due Tu 12/5
Th 11/23 Thanksgiving – No Class    
Tu 11/28 Information theory basics, entropy    
Th 11/30 Kullback-Leibler divergence    
Tu 12/5 Project Presentations   Final Project Reports Due