Score Matching for Truncated Density Estimation on a Manifold

Daniel J. Williams, Song Liu
Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022, PMLR 196:312-321, 2022.

Abstract

When observations are truncated, we are limited to an incomplete picture of our dataset. Recent methods deal with truncated density estimation problems by turning to score matching, where the access to the intractable normalising constant is not required. We present a novel extension to truncated score matching for a Riemannian manifold. Applications are presented for the von Mises-Fisher and Kent distributions on a two dimensional sphere in R3, as well as a realworld application of extreme storm observations in the USA. In simulated data experiments, our score matching estimator is able to approximate the true parameter values with a low estimation error and shows improvements over a maximum likelihood estimator.

Cite this Paper

BibTeX
@InProceedings{pmlr-v196-williams22a, title = {Score Matching for Truncated Density Estimation on a Manifold}, author = {Williams, Daniel J. and Liu, Song}, booktitle = {Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022}, pages = {312--321}, year = {2022}, editor = {Cloninger, Alexander and Doster, Timothy and Emerson, Tegan and Kaul, Manohar and Ktena, Ira and Kvinge, Henry and Miolane, Nina and Rieck, Bastian and Tymochko, Sarah and Wolf, Guy}, volume = {196}, series = {Proceedings of Machine Learning Research}, month = {25 Feb--22 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v196/williams22a/williams22a.pdf}, url = {https://proceedings.mlr.press/v196/williams22a.html}, abstract = {When observations are truncated, we are limited to an incomplete picture of our dataset. Recent methods deal with truncated density estimation problems by turning to score matching, where the access to the intractable normalising constant is not required. We present a novel extension to truncated score matching for a Riemannian manifold. Applications are presented for the von Mises-Fisher and Kent distributions on a two dimensional sphere in R3, as well as a realworld application of extreme storm observations in the USA. In simulated data experiments, our score matching estimator is able to approximate the true parameter values with a low estimation error and shows improvements over a maximum likelihood estimator.} }
Endnote
%0 Conference Paper %T Score Matching for Truncated Density Estimation on a Manifold %A Daniel J. Williams %A Song Liu %B Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022 %C Proceedings of Machine Learning Research %D 2022 %E Alexander Cloninger %E Timothy Doster %E Tegan Emerson %E Manohar Kaul %E Ira Ktena %E Henry Kvinge %E Nina Miolane %E Bastian Rieck %E Sarah Tymochko %E Guy Wolf %F pmlr-v196-williams22a %I PMLR %P 312--321 %U https://proceedings.mlr.press/v196/williams22a.html %V 196 %X When observations are truncated, we are limited to an incomplete picture of our dataset. Recent methods deal with truncated density estimation problems by turning to score matching, where the access to the intractable normalising constant is not required. We present a novel extension to truncated score matching for a Riemannian manifold. Applications are presented for the von Mises-Fisher and Kent distributions on a two dimensional sphere in R3, as well as a realworld application of extreme storm observations in the USA. In simulated data experiments, our score matching estimator is able to approximate the true parameter values with a low estimation error and shows improvements over a maximum likelihood estimator.
APA
Williams, D.J. & Liu, S.. (2022). Score Matching for Truncated Density Estimation on a Manifold. Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022, in Proceedings of Machine Learning Research 196:312-321 Available from https://proceedings.mlr.press/v196/williams22a.html.

Related Material