Expected path length on random manifolds

Abstract

Manifold learning seeks a low dimensional representation that faithfully captures the essence of data. Current methods can successfully learn such representations, but do not provide a meaningful set of operations that are associated with the representation. Working towards operational representation learning, we endow the latent space of a large class of generative models with a random Riemannian metric, which provides us with elementary operators. As computational tools are unavailable for random Riemannian manifolds, we study deterministic approximations and derive tight error bounds on expected distances.

References in corpus (4)

• Auto-Encoding Variational Bayes
• Metrics for Probabilistic Geometries
• Only Bayes should learn a manifold (on the estimation of differential geometric structure from data)
• Random projections of random manifolds

Cited by in corpus (6)

• Only Bayes should learn a manifold (on the estimation of differential geometric structure from data)
• Variational Autoencoders with Riemannian Brownian Motion Priors
• A prior-based approximate latent Riemannian metric
• Geometrically Enriched Latent Spaces
• Identifying latent distances with Finslerian geometry
• Pulling back information geometry