Riemannian Metric Learning via Optimal Transport
Name
Scarvelis-scarv-SM-EECS-2022-thesis.pdf
Description
Thesis PDF
Size
25.63 MB
Format
Adobe PDF
Checksum (MD5)
2a8ab3a15664eabc47dea2d7d5ac83f1
Author(s)
Scarvelis, Christopher
Advisor(s)
Solomon, Justin
Date Issued
September 2022
Publisher
Massachusetts Institute of Technology
Abstract
We introduce an optimal transport-based model for learning a metric tensor from cross-sectional samples of evolving probability measures on a common Riemannian manifold. We neurally parametrize the metric as a spatially-varying matrix field and efficiently optimize our model's objective using backpropagation. Using this learned metric, we can nonlinearly interpolate between probability measures and compute geodesics on the manifold. We show that metrics learned using our method improve the quality of trajectory inference on scRNA and bird migration data at the cost of little additional cross-sectional data.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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