Unsupervised Ground Metric Learning Using Wasserstein Singular Vectors
Speaker: Geert-Jan Huizing (PhD student at École normale supérieure PSL)
Title: Unsupervised Ground Metric Learning Using Wasserstein Singular Vectors
Abstract: Using single-cell biology to motivate the method, I will introduce the concept of Wasserstein Singular Vectors [1], a natural way to simultaneously define Optimal Transport (OT) distances both on samples (e.g. cells) and on features (e.g. genes).
OT lifts a distance between features (the "ground metric") to a geometrically meaningful distance between samples. However, there is usually no straightforward choice of ground metric, especially in unsupervised settings. Wasserstein Singular Vectors are a canonical way to perform usupervised ground metric learning, which is fundamental to enabling data-driven applications of OT.
I will show that Wasserstein Singular Vectors emerge naturally as positive singular vectors of the function mapping ground metrics to OT distances. I will provide theoretical properties of these singular vectors, and discuss the various computational schemes that we studied. I will illustrate this with results on a single-cell RNA-sequencing dataset.
[1] Geert-Jan Huizing, Laura Cantini, Gabriel Peyré. Proceedings of the 39th International Conference on Machine Learning, PMLR 162:9429-9443, 2022.
More information: https://gjhuizing.github.io/
Talk in room M7 101 (Campus Monod, ENS de Lyon)
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