May 18, 2022 Machine Learning

Entropic Gromov-Wasserstein between Gaussian Distributions

  • 15 minutes
  • Khang Le, Dung Le, Huy Nguyen, Dat Do, Tung Pham, Nhat Ho.

  • ICML 2022
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Abstract

We study the entropic Gromov-Wasserstein and its unbalanced version between (unbalanced) Gaussian distributions with different dimensions. When the metric is the inner product, which we refer to as inner product Gromov-Wasserstein (IGW), we demonstrate that the optimal transportation plans of entropic IGW and its unbalanced variant are (unbalanced) Gaussian distributions. Via an application of von Neumann’s trace inequality, we obtain closed-form expressions for the entropic IGW between these Gaussian distributions. Finally, we consider an entropic inner product Gromov-Wasserstein barycenter of multiple Gaussian distributions. We prove that the barycenter is a Gaussian distribution when the entropic regularization parameter is small. We further derive a closed-form expression for the covariance matrix of the barycenter.

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  • 15 minutes
  • Khang Le, Dung Le, Huy Nguyen, Dat Do, Tung Pham, Nhat Ho.

  • ICML 2022
Share

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