Expected path length on random manifolds

2019/08/20 by David Eklund, Søren Hauberg, Eklund, David +1 · 1 citation
Computer Science · #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Generative Adversarial Networks and Image Synthesis #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Neural Networks and Applications

paper · pdf · doi:10.48550/arxiv.1908.07377

openalex publication_date 2019/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Metrics for Probabilistic Geometries
• Auto-Encoding Variational Bayes
• Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
• Random projections of random manifolds
• Only Bayes should learn a manifold (on the estimation of differential geometric structure from data)
• High-dimensional p-norms
• Variational Inference: A Review for Statisticians

Cited by

• Geometrically Enriched Latent Spaces

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