A prior-based approximate latent Riemannian metric

Georgios Arvanitidis, Bogdan M. Georgiev, Bernhard Schölkopf
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:4634-4658, 2022.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-arvanitidis22a, title = { A prior-based approximate latent Riemannian metric }, author = {Arvanitidis, Georgios and Georgiev, Bogdan M. and Sch\"olkopf, Bernhard}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {4634--4658}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/arvanitidis22a/arvanitidis22a.pdf}, url = {https://proceedings.mlr.press/v151/arvanitidis22a.html}, 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. } }
Endnote
%0 Conference Paper %T A prior-based approximate latent Riemannian metric %A Georgios Arvanitidis %A Bogdan M. Georgiev %A Bernhard Schölkopf %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-arvanitidis22a %I PMLR %P 4634--4658 %U https://proceedings.mlr.press/v151/arvanitidis22a.html %V 151 %X 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.
APA
Arvanitidis, G., Georgiev, B.M. & Schölkopf, B.. (2022). A prior-based approximate latent Riemannian metric . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:4634-4658 Available from https://proceedings.mlr.press/v151/arvanitidis22a.html.

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