A prior-based approximate latent Riemannian metric

Georgios Arvanitidis, Bogdan Georgiev, Bernhard Scholkopf

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Abstract

Stochastic generative models enable us to capture the geometric structure of a data manifold lying in a high dimensional space through a Riemannian metric in the latent space. However, its practical use is rather limited mainly due to inevitable functionality problems and computational complexity. In this work we propose a surrogate conformal Riemannian metric in the latent space of a generative model that is simple, efficient and robust. This metric is based on a learnable prior that we propose to learn using a basic energy-based model. We theoretically analyze the behavior of the proposed metric and show that it is sensible to use in practice. We demonstrate experimentally the efficiency and robustness, as well as the behavior of the new approximate metric. Also, we show the applicability of the proposed methodology for data analysis in the life sciences.
Original languageEnglish
Title of host publicationProceedings of the 25th International Conference on Artificial Intelligence and Statistics
Number of pages25
PublisherInternational Machine Learning Society (IMLS)
Publication date2022
Publication statusPublished - 2022
Event25th International Conference on Artificial Intelligence and Statistics - Virtual Conference
Duration: 28 Mar 202230 Mar 2022
Conference number: 25
https://aistats.org/aistats2022/
https://proceedings.mlr.press/v151/

Conference

Conference25th International Conference on Artificial Intelligence and Statistics
Number25
LocationVirtual Conference
Period28/03/202230/03/2022
Internet address
SeriesProceedings of Machine Learning Research
Volume151
ISSN2640-3498

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