Optimal Transport part 1 Marco Cuturi MLSS 2020 Tübingen

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Table of Contents (powered by https://videoken.com) • 0:00:00 Optimal Transport • 0:02:52 Why Optimal Transport? • 0:07:11 Optimal Transport in Data Science • 0:11:17 Short Course Outline • 0:12:42 Introduction to OT • 0:13:39 Origins: Monger Problem (1781) • 0:22:09 Kantorovich Problem • 0:27:38 Why Optimal Transport? • 0:34:46 Mathematical Formalism • 0:35:12 OT: Nature's way to move particles • 0:39:48 Monger Problem • 0:48:03 Example 2: Monge-Ampere Equation • 0:50:42 Kantorovich Relaxation • 0:52:50 Kantorovich Problem • 0:59:15 Deriving Kantorovich Duality • 1:02:12 Deriving Kantorovich Duality Let 4, 1 : 0 - R, and P E II( M, • 1:08:44 Wasserstein Distances • 1:10:46 Kantorovich Problem • 1:12:35 Kantorovich Duality • 1:13:18 transforms • 1:20:21 transforms, WI • 1:21:52 Links between Monger Kantorovic • 1:24:18 Optimal Transport Geometry • 1:26:22 Variational OT Problems in ML • 1:27:40 2. Computing OT exactly

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