Learning Bijective Feature Maps for Linear ICA

Alexander Camuto, Matthew Willetts, Chris Holmes, Brooks Paige, Stephen Roberts
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:3655-3663, 2021.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-camuto21b, title = { Learning Bijective Feature Maps for Linear ICA }, author = {Camuto, Alexander and Willetts, Matthew and Holmes, Chris and Paige, Brooks and Roberts, Stephen}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {3655--3663}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/camuto21b/camuto21b.pdf}, url = {https://proceedings.mlr.press/v130/camuto21b.html}, 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. } }
Endnote
%0 Conference Paper %T Learning Bijective Feature Maps for Linear ICA %A Alexander Camuto %A Matthew Willetts %A Chris Holmes %A Brooks Paige %A Stephen Roberts %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-camuto21b %I PMLR %P 3655--3663 %U https://proceedings.mlr.press/v130/camuto21b.html %V 130 %X 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.
APA
Camuto, A., Willetts, M., Holmes, C., Paige, B. & Roberts, S.. (2021). Learning Bijective Feature Maps for Linear ICA . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:3655-3663 Available from https://proceedings.mlr.press/v130/camuto21b.html.

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