David Alvarez-Melis
(he/him/his)
Assistant Professor, Harvard University (SEAS)
150 Western Av. Room 2-332, Allston MA 02134
[three initials]@seas.harvard.edu
CS 2840 — Optimal Transport for Machine Learning
Harvard, Fall 2025
A graduate-level introduction to optimal transport (OT) and its role in modern machine learning. The course covers OT foundations (Monge and Kantorovich formulations, Wasserstein distances, duality), computational methods (entropic regularization, Sinkhorn, dynamic OT), and applications across generative modeling, domain adaptation, representation learning, and distributional alignment.
| # | Title | Date | Format |
|---|---|---|---|
| 1 | Introduction | Sep 2 | HTML |
| 2 | Foundations, Monge, Brenier | Sep 4 | HTML |
| 3 | Kantorovich, Couplings | Sep 9 | HTML |
| 4 | Wasserstein, Duality | Sep 11 | HTML |
| 5 | c-transforms, duality, entropy regularization | Sep 16 | HTML |
| 6 | Entropic OT, continued | Sep 18 | HTML |
| 7 | Sinkhorn Divergences | Sep 23 | HTML |
| 8 | Dynamic OT, Part I | Sep 25 | HTML |
| 9 | Dynamic OT, Part II | Sep 30 | HTML |
| 10 | OT vs Divergences | Oct 2 | HTML |
| 11 | OT as a Loss Function | Oct 7 | HTML |
| 12 | Sliced Optimal Transport (guest: Kimia Nadjahi) | Oct 9 | pending |
| 13 | Extensions | Oct 14 | HTML |
| 14 | The Riemannian Structure of the 2-Wasserstein Distance: Gradient Flows and Linearization (guest: Katy Craig) | Oct 16 | pending |
| 15 | Optimal Transport for Graph Representation: Unsupervised Learning, Graph Prediction and Neural OT Solvers (guest: Rémi Flamary) | Oct 21 | pending |
| 16 | Domain Adaptation: Old and New with Optimal Transport (guest: Nicolas Courty) | Oct 23 | pending |
| 17 | Distributional Preference Alignment of LLMs via Optimal Transport (guest: Youssef Mroueh) | Nov 3 | pending |
| 18 | Optimal Transport and Flow Matching (guest: Marco Cuturi) | Nov 6 | pending |
| 19 | Gromov-Wasserstein Alignment: Statistics, Computation, and Geometry (guest: Ziv Goldfeld) | Nov 20 | pending |