Course Structure

We will cover non-Euclidean machine learning in three main categories: learning on non-Euclidean domains, learning non-Euclidean embeddings and working in non-Euclidean parameter spaces. In addition to the standard optimization tools for enabling these methods, we will also cover Bayesian methods and in particular sampling on non-Euclidean domains. A quick taxonomy of this course is given below:

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Detailed Schedule

Date Description Suggested Readings Events Instructor
Week 1 / Monday, September 14 Introduction: Syllabus, motivation, history & basics of geometry - - Tolga
Week 1 / Wednesday, September 16 Basics of geometry of curves and surfaces - - Tolga
Week 2 / Monday, September 21 Review of differential geometry (topological manifold, smooth manifold, coordinates, charts and atlases) - - Tolga
Week 2 / Wednesday, September 23 Review of Riemannian geometry (riemannian metric, geodesics, examples of constant curvature spaces) Elements of General Relativity, MA430 Notes by Lia Vas - Tolga
Week 2 / Friday, September 25 Office Hour - HW1 Out Anthea, Tolga, Ines
Week 3 / Monday, September 28 Optimization on Riemannian manifolds I (RSGD, riemannian line search) Chapters 3 & 4 in Optimization on Smooth Manifolds - Tolga
Week 3 / Wednesday, September 30 Algorithms on Riemannian manifolds (PCA, Karcher mean, PGA, MDS and etc.) Karcher Mean, Sphere and Hyperboloid Example, PGA, h-MDS - Guest Lecture: Frederic Sala
Week 3 / Friday, October 2 Office Hour - - Anthea, Tolga, Ines
Week 4 / Monday, October 5 Matrix Manifolds and Applications in Computer Vision I Edelman et al. 1998, Optimization Algorithms on Matrix Manifolds (Ch. 1-4) - Tolga
Week 4 / Wednesday, October 7 Probability on Riemannian manifolds & Sampling Intrinsic Statistics on Riemannian Manifolds - Guest Lecture: Nina Miolane
Week 4 / Friday, October 9 Office Hour - HW2 Out, iPython Notebook Anthea, Tolga, Ines
Week 5 / Monday, October 12 Riemannian Bayesian Inference [Recipe for SG-MCMC], [SG-GMC], [Birdal & Simsekli'19], [Birdal & et al.'18], [HMC] - Tolga
Week 5 / Wednesday, October 14 [9am PDT] Second Order Methods in Riemannian Optimization - - Guest Lecture (9am PDT): Nicolas Boumal
Week 5 / Friday, October 16 Office Hour - - Anthea, Tolga, Ines
Week 6 / Monday, October 19 [9am PDT] From Manifolds to Graphs: Geodesics Convergence of Geodesics, IsoMap paper - Ines
Week 6 / Wednesday, October 21 [9am PDT] From Manifolds to Graphs: Laplacian Convergence of the Laplacian, SSL, Laplacian Eigenmaps, Section IV in GDL Survey, Spectral Clustering - Ines
Week 6 / Friday, October 23 Office Hour - HW2 Due, Project Proposal Out Anthea, Tolga, Ines
Week 7 / Monday, October 26 [9am PDT] From Graphs to Manifolds: Shallow Graph Embeddings Deep Walk, Sections 1-4 in Graph Survey, Poincare embeddings, Product-space embeddings - Ines
Week 7 / Wednesday, October 28 [9am PDT] From Graphs to Manifolds: Graph Neural Networks Spectral Graph CNN, Section III, V and VI in GDL Survey, ChebyNet, GCN, Sections 5-7 in Graph Survey, Hyperbolic GCN - Ines
Week 7 / Friday, October 30 Office Hour - - Anthea, Tolga, Ines
Week 8 / Monday, November 2 Computer Vision Applications: Shape Modeling - - Guest Lecture: Emanuele Rodola
Week 8 / Wednesday, November 4 Computer Vision Applications: Point Clouds - Tolga
Week 8 / Friday, November 6 Office Hour - Anthea, Tolga, Ines
Week 9 / Monday, November 9 Laplace-Beltrami Operators and Intrinsic Descriptors on Manifolds - - Guest Lecture: Leonidas Guibas
Week 9 / Wednesday, November 11 Normalizing Flows for Manifolds - Guest Lecture: Aaron Lou
Week 9 / Friday, November 13 Office Hour - Final Project Due
Week 10 / Monday, November 16 Project Presentations - - -
Week 10 / Wednesday, November 18 Project Presentations - - -