Scalably computing metric magnitude

Steve Huntsman, Jewell B. Thomas, Cynthia Ukawu
Proceedings of the 2nd Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2026), PMLR 334(2):4-24, 2026.

Abstract

Applications of metric magnitude often rely on numerically exact results in order to exploit a connection with information theory. We examine various approaches for scaling the dense linear algebra involved and identify hierarchical low-rank solvers as a preferred approach, with a clear path to scales of $10^5$ points on a single powerful workstation, and larger scales for clusters and/or supercomputers using our containerized C++/MPI pipeline.

Cite this Paper

BibTeX
@InProceedings{pmlr-v334-huntsman26a, title = {Scalably computing metric magnitude}, author = {Huntsman, Steve and Thomas, Jewell B. and Ukawu, Cynthia}, booktitle = {Proceedings of the 2nd Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2026)}, pages = {4--24}, year = {2026}, editor = {Berman, Eddie and Bernárdez, Guillermo and Chen, Samantha and Cloninger, Alex and Doster, Timothy and Emerson, Tegan and Grigsby, J. Elisenda and Kvinge, Henry and Lawrence, Hannah and Marrinan, Tim and Myers, Audun and Papillon, Mathilde and Tahmasebi, Behrooz and Telyatnikov, Lev and Walters, Robin and Weber, Melanie and Xie, YuQing and Yeats, Eric}, volume = {334}, number = {2}, series = {Proceedings of Machine Learning Research}, month = {18--20 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v334/main/assets/huntsman26a/huntsman26a.pdf}, url = {https://proceedings.mlr.press/v334/huntsman26a.html}, abstract = {Applications of metric magnitude often rely on numerically exact results in order to exploit a connection with information theory. We examine various approaches for scaling the dense linear algebra involved and identify hierarchical low-rank solvers as a preferred approach, with a clear path to scales of $10^5$ points on a single powerful workstation, and larger scales for clusters and/or supercomputers using our containerized C++/MPI pipeline.} }
Endnote
%0 Conference Paper %T Scalably computing metric magnitude %A Steve Huntsman %A Jewell B. Thomas %A Cynthia Ukawu %B Proceedings of the 2nd Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2026) %C Proceedings of Machine Learning Research %D 2026 %E Eddie Berman %E Guillermo Bernárdez %E Samantha Chen %E Alex Cloninger %E Timothy Doster %E Tegan Emerson %E J. Elisenda Grigsby %E Henry Kvinge %E Hannah Lawrence %E Tim Marrinan %E Audun Myers %E Mathilde Papillon %E Behrooz Tahmasebi %E Lev Telyatnikov %E Robin Walters %E Melanie Weber %E YuQing Xie %E Eric Yeats %F pmlr-v334-huntsman26a %I PMLR %P 4--24 %U https://proceedings.mlr.press/v334/huntsman26a.html %V 334 %N 2 %X Applications of metric magnitude often rely on numerically exact results in order to exploit a connection with information theory. We examine various approaches for scaling the dense linear algebra involved and identify hierarchical low-rank solvers as a preferred approach, with a clear path to scales of $10^5$ points on a single powerful workstation, and larger scales for clusters and/or supercomputers using our containerized C++/MPI pipeline.
APA
Huntsman, S., Thomas, J.B. & Ukawu, C.. (2026). Scalably computing metric magnitude. Proceedings of the 2nd Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2026), in Proceedings of Machine Learning Research 334(2):4-24 Available from https://proceedings.mlr.press/v334/huntsman26a.html.

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