Topics on Optimal Transport in Machine Learning and Shape Analysis

Course Info

Instructor Facundo Mémoli, m e m o l i @ m a t h . o s u . e d u
Course code CSE 5339 -- Spring 2018
Times: Thursdays 1.50 -- 3.40 pm
Location: BH 422.
Description: Optimal transport problems arisen the work of the french mathematician Gaspard Monge in the late 1700s. The original formulation was meant to model the optimal way of moving goods from a collection of sources to a collection of distribution points. The formulation was subsequently improved by the economist Leonid Kantorovich in the mid 1900s who found a more efficient linear programming relaxation.

In recent years ideas from optimal transport have been applied to problems in machine learning and geometric shape processing. This course will first cover the main ideas/concepts related to optimal transport, and will then explore several of its modern applications to ML and SA. Prerequisites: familiarity with discrete math/structures and interest in/familiarity with basic machine learning and shape analysis concepts.

Several possible research directions will be discussed.

Prerequisites: The course has minimal requisites: it is designed for students from Computer Science and Engineering, and Mathematics having knowledge of undergrad level math. Some knowledge of geometry will be useful, but not necessary. The course will provide the opportunity to explore different aspects of the material: interested students will have the opportunity of implementing some algorithms and/or exploring some research papers on different aspects of both the underlying mathematics and/or the algorithmic procedures.


Meeting 1 (1/11). First meeting.
Meeting 2 (1/18). Basics of OT.
Meeting 3 (1/25). Basics of OT.
Meeting 4 (2/1). Basics of OT.
Meeting 5 (2/8). Basics of OT.
Meeting 6 (2/15). Basics of OT.
Meeting 7 (2/22). Sinkhorn Distances: Lightspeed Computation of Optimal transportation distances. Woojin Kim. [report].
Meeting 8 (3/1). (1) Joint distribution optimal transportation for domain adaptation. Changhuang Wan. Slides. [report].
(2) Stochastic optimization for large scale OT. Sixiong You.
Slides. [report].
Meeting 9 (3/8). (1) Optimal Transport for Gaussian Mixture Models. Zach Lucas. Slides. [report].
(2) From optimal transport to generative modeling: the VEGAN cookbook. Cheng Xin.
Slides. [report].
Meeting 10 (3/22). (1). An Optimal Transport Approach to Robust Reconstruction and Simplification of 2D Shapes. Kritika Singhal. Slides. [report].
(2) Geometric Inference for Measures based on Distance Functions . Zhengchao Wan.
Slides. [report].
Meeting 11 (3/29). (1) Algorithms to automatically quantify the geometric similarity of anatomical surfaces. Ying Yin. Slides. [report].
(2) Theory of entropic regularization. Samir Chowdhury.
Slides. [report].
Meeting 12 (4/5). (1) Olivier's Ricci curvature and applications. Sunhyuk Lim. Slides. [report].
(2) Sliced Wasserstein distance for persistence diagrams. Xiao Zha.
Slides. [report].
Meeting 13 (4/12). (1) Convex color image segmentation with OT. Siyang Zhang. Slides. [report].
(2) EMD and embedding into l1. Tim Carpenter.
Slides. [report].
Meeting 14 (4/19). (1) Brenier's polar factorization and McCann's generalization. Osman Okutan. Slides. [report].