Manifold Learning by Mixture Models of VAEs for Inverse Problems

arXiv:2303.15244v2 Announce Type: replace-cross
Abstract: Representing a manifold of very high-dimensional data with generative models has been shown to be computationally efficient in practice. However, this requires that the data manifold admits a global parameterization. In order to represent manifolds of arbitrary topology, we propose to learn a mixture model of variational autoencoders. Here, every encoder-decoder pair represents one chart of a manifold. We propose a loss function for maximum likelihood estimation of the model weights and choose an architecture …

abstract arxiv cs.lg data generative generative models global however learn manifold practice replace stat.ml topology type