Geometric Dataset Distances via Optimal Transport (2002.02923v1)

Abstract: 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.

• The paper defines a principled distance metric using Wasserstein optimal transport to compare datasets, even with disjoint label sets.
• The paper scales up optimal transport computations with algorithmic approximations to efficiently handle large datasets.
• The paper’s empirical validation confirms that higher geometric similarity between datasets correlates with improved transfer learning performance.

Geometric Dataset Distances via Optimal Transport: A Formal Analysis

The paper "Geometric Dataset Distances via Optimal Transport" addresses a pivotal issue in machine learning, particularly within domain adaptation and meta-learning: quantifying similarity between datasets. The authors propose a novel approach leveraging optimal transport (OT) theory for defining geometric dataset distances that are model-agnostic and do not necessitate any form of training. This contribution advances beyond heuristic methods, offering a theoretically grounded metric capable of comparing datasets even with disjoint label sets.

Summary of Contributions

The authors introduce several key contributions to the field:

1. Principled Definition of Dataset Distance: The paper proposes a distance metric between datasets by modeling the space of features and labels as distributions leveraging the Wasserstein distance. This approach allows for the expression of label similarities in terms of feature distributions, providing a distance metric that can compare datasets with completely different label sets.
2. Algorithmic Scale-up: Recognizing the computational challenges inherent in optimal transport calculations, the authors suggest algorithmic shortcuts and approximations to make the proposed metric scalable. This includes techniques to efficiently compute the distribution of characteristics within large datasets.
3. Empirical Validation: The authors demonstrate through a series of experiments on varied domains (e.g., image classification across mnist and usps, text classification using {bert} embeddings) that their proposed metric predicts transfer learning success effectively. The results corroborate the hypothesis that greater dataset similarity, according to their metric, correlates with improved transfer learning performance.

Theoretical and Practical Implications

From a theoretical standpoint, this paper extends the concept of optimal transport to incorporate label distributions in the computation of distances between datasets. The notion that datasets can be viewed as geometric objects with distributions over their labels, and hence compared using Wasserstein-type distances, is particularly robust. The authors also prove the validity of the proposed metric as a bona fide distance measure by establishing connections with the Gelbrich bound.

Practically, the introduction of this metric provides a tool that researchers and practitioners can use to strategically select source datasets for pretraining models—optimizing transfer learning initiatives without resorting to exhaustive trial-and-error processes. The paper suggests possible applications in efficient data augmentation as well, potentially guiding augmentation strategies by aligning transformed datasets closer to the target domain.

Speculation on AI Future Developments

Looking forward, dataset distance metrics such as the one presented could become integral to automated machine learning pipelines, guiding everything from dataset selection to feature engineering and augmentation. This work lays the groundwork for more sophisticated, data-driven approaches to model transferability assessment, potentially reducing computational costs in model training and improving the accuracy and adaptability of AI systems.

As advancements continue in the computation and application of Wasserstein distances, and as datasets and models grow increasingly complex, this theoretical underpinning might inspire further explorations into hierarchical OT distances and incorporate more dynamic forms of distributions, such as Gaussian Processes or mixture models. Future developments could also involve synergizing such metrics with deep learning architectures, where both structure and geometry of data are leveraged simultaneously for cross-domain adaptation.

In conclusion, the paper by Alvarez-Melis and Fusi contributes significantly to understanding and applying optimal transport theory to measure dataset similarity in a computationally feasible and theoretically sound manner. This bridges a gap in machine learning practice, paving the way for smarter, geometry-aware AI systems.