Expected path length on random manifolds

Understand

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.