A prior-based approximate latent Riemannian metric
This work addresses the practical limitations of using Riemannian metrics in generative models for data analysis, particularly in life sciences, but appears incremental as it builds on existing methods with a new approximation.
The authors tackled the complexity and limited practicality of Riemannian metrics in latent spaces of generative models by proposing a surrogate conformal Riemannian metric based on a learnable prior, demonstrating its efficiency, robustness, and applicability in life sciences data analysis.
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.