Geometric Dataset Distances via Optimal Transport
This provides a more robust and interpretable method for comparing datasets, benefiting tasks like domain adaptation and meta-learning, though it is incremental as it builds on existing optimal transport theory.
The paper tackled the problem of quantifying task similarity in machine learning by proposing a model-agnostic dataset distance based on optimal transport, which does not require training and can compare datasets with disjoint labels, showing it correlates well with transfer learning hardness in experiments.
The notion of task similarity is at the core of various machine learning paradigms, such as domain adaptation and meta-learning. Current methods to quantify it are often heuristic, make strong assumptions on the label sets across the tasks, and many are architecture-dependent, relying on task-specific optimal parameters (e.g., require training a model on each dataset). In this work we propose an alternative notion of distance between datasets that (i) is model-agnostic, (ii) does not involve training, (iii) can compare datasets even if their label sets are completely disjoint and (iv) has solid theoretical footing. This distance relies on optimal transport, which provides it with rich geometry awareness, interpretable correspondences and well-understood properties. Our results show that this novel distance provides meaningful comparison of datasets, and correlates well with transfer learning hardness across various experimental settings and datasets.