A Riemannian Approach to Ground Metric Learning for Optimal Transport
This work addresses the challenge of enhancing OT-based distances for domain adaptation in machine learning, representing an incremental improvement by focusing on metric learning within an existing framework.
The paper tackles the problem of learning a suitable latent ground metric for optimal transport (OT) distances by parameterizing it with a symmetric positive definite matrix and using Riemannian geometry, resulting in improved performance in OT-based domain adaptation as shown in empirical results.
Optimal transport (OT) theory has attracted much attention in machine learning and signal processing applications. OT defines a notion of distance between probability distributions of source and target data points. A crucial factor that influences OT-based distances is the ground metric of the embedding space in which the source and target data points lie. In this work, we propose to learn a suitable latent ground metric parameterized by a symmetric positive definite matrix. We use the rich Riemannian geometry of symmetric positive definite matrices to jointly learn the OT distance along with the ground metric. Empirical results illustrate the efficacy of the learned metric in OT-based domain adaptation.