Geometric Interpretation to Generative Models and Optimal Transportation, M.Sc. Thesis Sharif University of Technology ; Bahraini, Alireza (Supervisor)
Abstract
As the core of this thesis, we express the relation between optimal transportation and convex geometry especially the variational approach to solve Alexandrov problem, which leads to a geometric interpretation to adversarial models and propose a novel framework for these models. Along the way, we peruse generative adversarial networks from optimal transportation view and show that generator calculates the transportation map and the discriminator computes Wasserestein distance, which is equivalent to Kantorovich potential. By using optimal mass transportation theory and choosing an especial cost function c, we see that the generator and discriminator are equivalent. Therefore, once the...
Cataloging briefGeometric Interpretation to Generative Models and Optimal Transportation, M.Sc. Thesis Sharif University of Technology ; Bahraini, Alireza (Supervisor)
Abstract
As the core of this thesis, we express the relation between optimal transportation and convex geometry especially the variational approach to solve Alexandrov problem, which leads to a geometric interpretation to adversarial models and propose a novel framework for these models. Along the way, we peruse generative adversarial networks from optimal transportation view and show that generator calculates the transportation map and the discriminator computes Wasserestein distance, which is equivalent to Kantorovich potential. By using optimal mass transportation theory and choosing an especial cost function c, we see that the generator and discriminator are equivalent. Therefore, once the...
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