Lightspeed Geometric Dataset Distance via Sliced Optimal Transport
This provides a fast, scalable tool for dataset comparison in machine learning, useful for tasks like transfer learning and data augmentation, though it is an incremental improvement over existing optimal transport methods.
The paper tackles the problem of comparing datasets efficiently by introducing sliced optimal transport dataset distance (s-OTDD), a model-agnostic method that achieves near-linear computational complexity in data points and features, and shows strong correlation with transfer learning performance gaps and classification accuracy in data augmentation.
We introduce sliced optimal transport dataset distance (s-OTDD), a model-agnostic, embedding-agnostic approach for dataset comparison that requires no training, is robust to variations in the number of classes, and can handle disjoint label sets. The core innovation is Moment Transform Projection (MTP), which maps a label, represented as a distribution over features, to a real number. Using MTP, we derive a data point projection that transforms datasets into one-dimensional distributions. The s-OTDD is defined as the expected Wasserstein distance between the projected distributions, with respect to random projection parameters. Leveraging the closed form solution of one-dimensional optimal transport, s-OTDD achieves (near-)linear computational complexity in the number of data points and feature dimensions and is independent of the number of classes. With its geometrically meaningful projection, s-OTDD strongly correlates with the optimal transport dataset distance while being more efficient than existing dataset discrepancy measures. Moreover, it correlates well with the performance gap in transfer learning and classification accuracy in data augmentation.