Riemannian Metric Learning via Optimal Transport
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 b...
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| Format: | Thesis |
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Massachusetts Institute of Technology
2023
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| Online Access: | https://hdl.handle.net/1721.1/147268 https://orcid.org/0000-0001-8516-6189 |
| _version_ | 1826207500320374784 |
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| author | Scarvelis, Christopher |
| author2 | Solomon, Justin |
| author_facet | Solomon, Justin Scarvelis, Christopher |
| author_sort | Scarvelis, Christopher |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T13:50:36Z |
| format | Thesis |
| id | mit-1721.1/147268 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T13:50:36Z |
| publishDate | 2023 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1472682023-01-20T03:26:42Z Riemannian Metric Learning via Optimal Transport Scarvelis, Christopher Solomon, Justin Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science 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. 2023-01-19T18:41:40Z 2023-01-19T18:41:40Z 2022-09 2022-10-19T18:58:38.533Z Thesis https://hdl.handle.net/1721.1/147268 https://orcid.org/0000-0001-8516-6189 In Copyright - Educational Use Permitted Copyright MIT http://rightsstatements.org/page/InC-EDU/1.0/ application/pdf Massachusetts Institute of Technology |
| spellingShingle | Scarvelis, Christopher Riemannian Metric Learning via Optimal Transport |
| title | Riemannian Metric Learning via Optimal Transport |
| title_full | Riemannian Metric Learning via Optimal Transport |
| title_fullStr | Riemannian Metric Learning via Optimal Transport |
| title_full_unstemmed | Riemannian Metric Learning via Optimal Transport |
| title_short | Riemannian Metric Learning via Optimal Transport |
| title_sort | riemannian metric learning via optimal transport |
| url | https://hdl.handle.net/1721.1/147268 https://orcid.org/0000-0001-8516-6189 |
| work_keys_str_mv | AT scarvelischristopher riemannianmetriclearningviaoptimaltransport |