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In this paper we study generative modeling via autoencoders while using the elegant geometric properties of the optimal transport (OT) problem and the Wasserstein distances. We introduce Sliced-Wasserstein Autoencoders (SWAE), which are generative models that enable one to shape the distribution of the latent space into any samplable probability distribution without the need for training an adversarial network or defining a closed-form for the distribution. In short, we regularize the autoencoder loss with the sliced-Wasserstein distance between the distribution of the encoded training samples and a predefined samplable distribution. We show that the proposed formulation has an efficient numerical solution that provides similar capabilities to Wasserstein Autoencoders (WAE) and Variational Autoencoders (VAE), while benefiting from an embarrassingly simple implementation.
The Wasserstein distance and its variations, e.g., the sliced-Wasserstein (SW) distance, have recently drawn attention from the machine learning community. The SW distance, specifically, was shown to have similar properties to the Wasserstein distanc
Developing machine learning methods that are privacy preserving is today a central topic of research, with huge practical impacts. Among the numerous ways to address privacy-preserving learning, we here take the perspective of computing the divergenc
Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as a powerful discrepancy measure for probability distributions. The recent developments on alternative
While variational autoencoders have been successful generative models for a variety of tasks, the use of conventional Gaussian or Gaussian mixture priors are limited in their ability to capture topological or geometric properties of data in the laten
Sliced-Wasserstein distance (SW) and its variant, Max Sliced-Wasserstein distance (Max-SW), have been used widely in the recent years due to their fast computation and scalability even when the probability measures lie in a very high dimensional spac