2026-09-18T21:15:02Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1472682023-01-20T03:26:42Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Solomon, Justin
Scarvelis, Christopher
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2023-01-19T18:41:40Z
2023-01-19T18:41:40Z
2022-09
2022-10-19T18:58:38.533Z
https://hdl.handle.net/1721.1/147268
https://orcid.org/0000-0001-8516-6189
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.
S.M.
Massachusetts Institute of Technology
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http://rightsstatements.org/page/InC-EDU/1.0/
Riemannian Metric Learning via Optimal Transport
Thesis
application/pdf
Master
Master of Science in Electrical Engineering and Computer Science
Publication
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unknown
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<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.</Abstract>
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