Global Sinkhorn Autoencoder : Optimal Transport on the latent representation of the full dataset

Csiszárik, Adrián and Kiss, Melinda and Maga, Balázs and Matszangosz, Ákos and Varga, Dániel (2024) Global Sinkhorn Autoencoder : Optimal Transport on the latent representation of the full dataset. ANNALES UNIVERSITATIS SCIENTIARUM BUDAPESTINENSIS DE ROLANDO EOTVOS NOMINATAE SECTIO COMPUTATORICA, 57. pp. 101-115. ISSN 0138-9491

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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. 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. 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.

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