Nonlinear Isometric Manifold Learning for Injective Normalizing Flows
Machine Learning
2023-05-09 v2
Abstract
To model manifold data using normalizing flows, we employ isometric autoencoders to design embeddings with explicit inverses that do not distort the probability distribution. Using isometries separates manifold learning and density estimation and enables training of both parts to high accuracy. Thus, model selection and tuning are simplified compared to existing injective normalizing flows. Applied to data sets on (approximately) flat manifolds, the combined approach generates high-quality data.
Keywords
Cite
@article{arxiv.2203.03934,
title = {Nonlinear Isometric Manifold Learning for Injective Normalizing Flows},
author = {Eike Cramer and Felix Rauh and Alexander Mitsos and Raúl Tempone and Manuel Dahmen},
journal= {arXiv preprint arXiv:2203.03934},
year = {2023}
}
Comments
11 pages, 7 figures, 4 tables