Global Ground Metric Learning with Applications to scRNA data

TL;DR

This paper introduces a novel method for learning a global ground metric for optimal transport that leverages class labels at the distribution level, improving tasks like embedding, clustering, and classification in complex biological data.

Contribution

It presents a new approach to learn a global ground metric from distribution-level labels, addressing limitations of predefined and supervised metrics in optimal transport.

Findings

Enhanced accuracy in embedding, clustering, and classification tasks.

Effective application to multi-disease scRNA-seq data.

Improved interpretability of the learned metric.

Abstract

Optimal transport provides a robust framework for comparing probability distributions. Its effectiveness is significantly influenced by the choice of the underlying ground metric. Traditionally, the ground metric has either been (i) predefined, e.g., as the Euclidean distance, or (ii) learned in a supervised way, by utilizing labeled data to learn a suitable ground metric for enhanced task-specific performance. Yet, predefined metrics typically cannot account for the inherent structure and varying importance of different features in the data, and existing supervised approaches to ground metric learning often do not generalize across multiple classes or are restricted to distributions with shared supports. To address these limitations, we propose a novel approach for learning metrics for arbitrary distributions over a shared metric space. Our method provides a distance between individual points like a global metric, but requires only class labels on a distribution-level for training. The learned global ground metric enables more accurate optimal transport distances, leading to improved performance in embedding, clustering and classification tasks. We demonstrate the effectiveness and interpretability of our approach using patient-level scRNA-seq data spanning multiple diseases.