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The scarcity of labeled data is a long-standing challenge for many machinelearning tasks. We propose our gradient flow method to leverage the existingdataset (i.e., source) to generate new samples that are close to the dataset ofinterest (i.e., target). We lift both datasets to the space of probabilitydistributions on the feature-Gaussian manifold, and then develop a gradientflow method that minimizes the maximum mean discrepancy loss. To perform thegradient flow of distributions on the curved feature-Gaussian space, we unravelthe Riemannian structure of the space and compute explicitly the Riemanniangradient of the loss function induced by the optimal transport metric. Forpractical applications, we also propose a discretized flow, and provideconditional results guaranteeing the global convergence of the flow to theoptimum. We illustrate the results of our proposed gradient flow method onseveral real-world datasets and show our method can improve the accuracy ofclassification models in transfer learning settings.

Dynamic Flows on Curved Space Generated by Labeled Data