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Conference Papers Year : 2019

Sliced-Wasserstein Flows: Nonparametric Generative Modeling via Optimal Transport and Diffusions

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Abstract

By building upon the recent theory that estab- lished the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algo- rithm for learning the underlying distributions of complicated datasets and sampling from them. The proposed algorithm is based on a functional optimization problem, which aims at finding a measure that is close to the data distribution as much as possible and also expressive enough for generative modeling purposes. We formulate the problem as a gradient flow in the space of proba- bility measures. The connections between gradi- ent flows and stochastic differential equations let us develop a computationally efficient algorithm for solving the optimization problem. We provide formal theoretical analysis where we prove finite- time error guarantees for the proposed algorithm. To the best of our knowledge, the proposed algo- rithm is the first nonparametric IGM algorithm with explicit theoretical guarantees. Our experi- mental results support our theory and show that our algorithm is able to successfully capture the structure of different types of data distributions.
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Dates and versions

hal-02191302 , version 1 (23-07-2019)

Licence

Attribution - CC BY 4.0

Identifiers

  • HAL Id : hal-02191302 , version 1

Cite

Antoine Liutkus, Umut Ş Imşekli, Szymon Majewski, Alain Durmus, Fabian-Robert Stöter. Sliced-Wasserstein Flows: Nonparametric Generative Modeling via Optimal Transport and Diffusions. ICML 2019 - 36th International Conference on Machine Learning, Jun 2019, Long Beach, United States. ⟨hal-02191302⟩
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