1 min read

From optimal transport to generative modeling: the VEGAN cookbook

On Tuesday 9th of June Anthony Lee presented From optimal transport to generative modeling: the VEGAN cookbook. The abstract is given below:

We study unsupervised generative modeling in terms of the optimal transport (OT) problem between true (but unknown) data distribution PX and the latent variable model distribution PG. We show that the OT problem can be equivalently written in terms of probabilistic encoders, which are constrained to match the posterior and prior distributions over the latent space. When relaxed, this constrained optimization problem leads to a penalized optimal transport (POT) objective, which can be efficiently minimized using stochastic gradient descent by sampling from PX and PG. We show that POT for the 2-Wasserstein distance coincides with the objective heuristically employed in adversarial auto-encoders (AAE) [1], which provides the first theoretical justification for AAEs known to the authors. We also compare POT to other popular techniques like variational auto-encoders (VAE) [2]. Our theoretical results include (a) a better understanding of the commonly observed blurriness of images generated by VAEs, and (b) establishing duality between Wasserstein GAN [3] and POT for the 1-Wasserstein distance.