Abstract
Variational autoencoders (VAEs) and generative adversarial networks (GANs) enjoy an intuitive connection to manifold learning: in training the decoder/generator is optimized to approximate a homeomorphism between the data distribution and the sampling space. This is a construction that strives to define the data manifold. A major obstacle to VAEs and GANs, however, is choosing a suitable prior that matches the data topology. Well-known consequences of poorly picked priors are posterior and mode collapse. To our knowledge, no existing method sidesteps this user choice. Conversely, diffusion maps automatically infer the data topology and enjoy a rigorous connection to manifold learning, but do not scale easily or provide the inverse homeomorphism (i.e. decoder/generator). We propose a method (https://github.com/lihenryhfl/vdae) that combines these approaches into a generative model that inherits the asymptotic guarantees of diffusion maps while preserving the scalability of deep models. We prove approximation theoretic results for the dimension dependence of our proposed method. Finally, we demonstrate the effectiveness of our method with various real and synthetic datasets.
Original language | English |
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Title of host publication | Computer Vision – ECCV 2020 - 16th European Conference, Glasgow, 2020, Proceedings |
Editors | Andrea Vedaldi, Horst Bischof, Thomas Brox, Jan-Michael Frahm |
Publisher | Springer Science and Business Media Deutschland GmbH |
Pages | 362-378 |
Number of pages | 17 |
ISBN (Print) | 9783030585914 |
DOIs | |
State | Published - 2020 |
Externally published | Yes |
Event | 16th European Conference on Computer Vision, ECCV 2020 - Glasgow, United Kingdom Duration: 23 Aug 2020 → 28 Aug 2020 |
Publication series
Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 12368 LNCS |
ISSN (Print) | 0302-9743 |
ISSN (Electronic) | 1611-3349 |
Conference
Conference | 16th European Conference on Computer Vision, ECCV 2020 |
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Country/Territory | United Kingdom |
City | Glasgow |
Period | 23/08/20 → 28/08/20 |
Bibliographical note
Publisher Copyright:© 2020, Springer Nature Switzerland AG.
Funding
Acknowledgements. This work was supported by NSF DMS grants 1819222 and 1818945. AC is also partially supported by NSF (DMS-2012266), and Russell Sage Foundation (grant 2196). XC is also partially supported by NSF (DMS-1820827), NIH (Grant R01GM131642), and the Alfred P. Sloan Foundation.
Funders | Funder number |
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NSF DMS | 1818945, 1819222 |
National Science Foundation | DMS-2012266 |
National Institutes of Health | R01GM131642 |
Alfred P. Sloan Foundation | |
Russell Sage Foundation | DMS-1820827, 2196 |
Keywords
- Deep learning
- Generative models
- Image and video synthesis
- Manifold learning
- Unsupervised learning
- Variational inference