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Learning Bijective Feature Maps for Linear ICA

Camuto, A; Willetts, M; Paige, B; Holmes, C; Roberts, S; (2021) Learning Bijective Feature Maps for Linear ICA. In: Banerjee, A and Fukumizu, K, (eds.) Proceedings of The 24th International Conference on Artificial Intelligence and Statistics. (pp. pp. 3655-3663). PMLR: Proceedings of Machine Learning Research Green open access

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Abstract

Separating high-dimensional data like images into independent latent factors, i.e independent component analysis (ICA), remains an open research problem. As we show, existing probabilistic deep generative models (DGMs), which are tailor-made for image data, underperform on non-linear ICA tasks. To address this, we propose a DGM which combines bijective feature maps with a linear ICA model to learn interpretable latent structures for high-dimensional data. Given the complexities of jointly training such a hybrid model, we introduce novel theory that constrains linear ICA to lie close to the manifold of orthogonal rectangular matrices, the Stiefel manifold. By doing so we create models that converge quickly, are easy to train, and achieve better unsupervised latent factor discovery than flow-based models, linear ICA, and Variational Autoencoders on images.

Type: Proceedings paper
Title: Learning Bijective Feature Maps for Linear ICA
Event: 24th International Conference on Artificial Intelligence and Statistics (AISTATS)
Location: ELECTR NETWORK
Dates: 13 April 2021 - 15 April 2021
Open access status: An open access version is available from UCL Discovery
Publisher version: https://proceedings.mlr.press/v130/camuto21b.html
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/10133435
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