2021/06/07 by Dimitris Kalatzis, Kalatzis, Dimitris, Johan Ziruo Ye +7 · 2 citations
Computer Science · Mathematics · #AI in cancer detection #Artificial intelligence #Combinatorics #Computer science #Cover (algebra) #Digital Imaging for Blood Diseases #Dimensionality reduction #Distribution (mathematics) #Euclidean geometry #Euclidean space #Focus (optics) #Geography #Geometry #Information geometry #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Nonlinear dimensionality reduction #Prior probability #Pure mathematics #Sample (material) #Scale (ratio) #Space (punctuation) #Statistical manifold #Topological and Geometric Data Analysis #Topology (electrical circuits) #cs.LG #stat.ML
paper · pdf · doi:10.48550/arxiv.2106.03500
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2021/06/07 · arxiv created 2022/07/09 · arxiv updated 2022/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a framework for learning probability distributions on topologically non-trivial manifolds, utilizing normalizing flows. Current methods focus on manifolds that are homeomorphic to Euclidean space, enforce strong structural priors on the learned models or use operations that do not easily scale to high dimensions. In contrast, our method learns distributions on a data manifold by "gluing" together multiple local models, thus defining an open cover of the data manifold. We demonstrate the efficiency of our approach on synthetic data of known manifolds, as well as higher dimensional manifolds of unknown topology, where our method exhibits better sample efficiency and competitive or superior performance against baselines in a number of tasks.