Global sinkhorn autoencoder - optimal transport on the latent representation of the full dataset

Abstract. We propose an Optimal Transport (OT)-based generative model from the Wasserstein Autoencoder (WAE) family of models, with the following innovative property: the optimization of the latent point positions takes place over the full training dataset rather than over a minibatch.
Our contributions are the following:
    1. We define a new class of global Wasserstein Autoencoder models, and implement an Optimal Transport-based incarnation we call the Global Sinkhorn Autoencoder.
\( \hskip 5mm\)2. We implement several metrics for evaluating such models, both in the unsupervised setting, and in a semi-supervised setting, which are the following: the global OT loss, which measures the OT loss on the full test dataset; the reconstruction error on the full test dataset; a so-called covered area which measures how well the latent points are matched; and two types of clustering measures.
\( \hskip 5mm\)3. We demonstrate on specific complex prior distributions that global optimal transport improves the performance of generative models compared to minibatch-based baselines when evaluated by the previously listed metrics.