A prior-based approximate latent Riemannian metric

• URL: http://arxiv.org/abs/2103.05290v1
• Date: Tue, 9 Mar 2021 08:31:52 GMT
• Title: A prior-based approximate latent Riemannian metric
• Authors: Georgios Arvanitidis, Bogdan Georgiev, Bernhard Sch\"olkopf
• Abstract summary: We propose a surrogate conformal generative metric in the latent space of a generative model that is simple, efficient and robust. We theoretically analyze the behavior of the proposed metric and show that it is sensible to use in practice. Also, we show the applicability of the proposed methodology for data analysis in the life sciences.
• Score: 3.716965622352967
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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.

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