Learning Generative Models across Incomparable Spaces

Abstract

Generative Adversarial Networks have shown remarkable success in learning a distribution that faithfully recovers a reference distribution in its entirety. However, in some cases, we may want to only learn some aspects (e.g., cluster or manifold structure), while modifying others (e.g., style, orientation or dimension). In this work, we propose an approach to learn generative models across such incomparable spaces, and demonstrate how to steer the learned distribution towards target properties. A key component of our model is the Gromov-Wasserstein distance, a notion of discrepancy that compares distributions relationally rather than absolutely. While this framework subsumes current generative models in identically reproducing distributions, its inherent flexibility allows application to tasks in manifold learning, relational learning and cross-domain learning.

International Conference on Machine Learning (ICML)

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Cited by in corpus (10)

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• Sliced Gromov-Wasserstein
• Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey
• A Survey on Optimal Transport for Machine Learning: Theory and Applications
• Linear-Time Gromov Wasserstein Distances using Low Rank Couplings and Costs
• Gromov-Wasserstein Factorization Models for Graph Clustering
• Personalised Federated Learning On Heterogeneous Feature Spaces
• LSMI-Sinkhorn: Semi-supervised Mutual Information Estimation with Optimal Transport
• CO-Optimal Transport