Dynamic Flows on Curved Space Generated by Labeled Data

TL;DR

This paper introduces a gradient flow method on curved probability spaces to generate new data samples from limited labeled datasets, improving transfer learning accuracy.

Contribution

It develops a novel gradient flow approach on the Riemannian space of probability distributions, explicitly computing gradients for data augmentation in transfer learning.

Findings

Improves classification accuracy in transfer learning tasks.

Provides a discretized flow with convergence guarantees.

Demonstrates effectiveness on real-world datasets.

Abstract

The scarcity of labeled data is a long-standing challenge for many machine learning tasks. We propose our gradient flow method to leverage the existing dataset (i.e., source) to generate new samples that are close to the dataset of interest (i.e., target). We lift both datasets to the space of probability distributions on the feature-Gaussian manifold, and then develop a gradient flow method that minimizes the maximum mean discrepancy loss. To perform the gradient flow of distributions on the curved feature-Gaussian space, we unravel the Riemannian structure of the space and compute explicitly the Riemannian gradient of the loss function induced by the optimal transport metric. For practical applications, we also propose a discretized flow, and provide conditional results guaranteeing the global convergence of the flow to the optimum. We illustrate the results of our proposed gradient flow method on several real-world datasets and show our method can improve the accuracy of classification models in transfer learning settings.