Lightspeed Geometric Dataset Distance via Sliced Optimal Transport

TL;DR

This paper introduces s-OTDD, a fast, model- and embedding-agnostic dataset distance measure based on sliced optimal transport, which effectively compares datasets regardless of class labels or disjoint label sets.

Contribution

The paper proposes the novel s-OTDD method utilizing Moment Transform Projection for efficient dataset comparison without training or class label constraints.

Findings

s-OTDD correlates with optimal transport dataset distance

It is computationally efficient with near-linear complexity

It effectively predicts transfer learning and classification performance gaps

Abstract

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.