Improving Gaussian mixture latent variable model convergence with Optimal Transport

Benoit Gaujac, Ilya Feige, David Barber

Abstract: Generative models with both discrete and continuous latent variables are highly motivated by the structure of many real-world data sets. They present, however, subtleties in training often manifesting in the discrete latent variable not being leveraged. In this paper, we show why such models struggle to train using traditional log-likelihood maximization, and that they are amenable to training using the Optimal Transport framework of Wasserstein Autoencoders. We find our discrete latent variable to be fully leveraged by the model when trained, without any modifications to the objective function or significant fine tuning. Our model generates comparable samples to other approaches while using relatively simple neural networks, since the discrete latent variable carries much of the descriptive burden. Furthermore, the discrete latent provides significant control over generation.

Keywords: optimal transport, wasserstein autoencoder, variational autoencoder, latent variable modeling, generative modeling, discrete latent variables

TL;DR: This paper shows that the Wasserstein distance objective enables the training of latent variable models with discrete latents in a case where the Variational Autoencoder objective fails to do so.