eprintid: 10195706 rev_number: 7 eprint_status: archive userid: 699 dir: disk0/10/19/57/06 datestamp: 2024-08-15 14:11:09 lastmod: 2024-08-15 14:11:09 status_changed: 2024-08-15 14:11:09 type: article metadata_visibility: show sword_depositor: 699 creators_name: Alberti, Giovanni S creators_name: Hertrich, Johannes creators_name: Santacesaria, Matteo creators_name: Sciutto, Silvia title: Manifold Learning by Mixture Models of VAEs for Inverse Problems ispublished: pub divisions: UCL divisions: B04 divisions: F48 keywords: Manifold learning, mixture models, variational autoencoders, Riemannian optimization, inverse problems note: This work is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) License. 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 that provides us the analytical expression of the charts and of their inverses. Once the manifold is learned, we use it for solving inverse problems by minimizing a data fidelity term restricted to the learned manifold. To solve the arising minimization problem we propose a Riemannian gradient descent algorithm on the learned manifold. We demonstrate the performance of our method for low-dimensional toy examples as well as for deblurring and electrical impedance tomography on certain image manifolds. date: 2024 date_type: published publisher: Microtome Publishing official_url: https://www.jmlr.org/papers/v25/23-0396.html oa_status: green full_text_type: pub language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 2304290 lyricists_name: Hertrich, Johannes lyricists_id: JHERT98 actors_name: Hertrich, Johannes actors_id: JHERT98 actors_role: owner funding_acknowledgements: EP/V026259/1 [Engineering and Physical Sciences Research Council] full_text_status: public publication: Journal of Machine Learning Research volume: 25 article_number: 202 citation: Alberti, Giovanni S; Hertrich, Johannes; Santacesaria, Matteo; Sciutto, Silvia; (2024) Manifold Learning by Mixture Models of VAEs for Inverse Problems. Journal of Machine Learning Research , 25 , Article 202. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/10195706/1/23-0396.pdf