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Separating high-dimensional data like images into independent latent factors,i.e independent component analysis (ICA), remains an open research problem. Aswe show, existing probabilistic deep generative models (DGMs), which aretailor-made for image data, underperform on non-linear ICA tasks. To addressthis, we propose a DGM which combines bijective feature maps with a linear ICAmodel to learn interpretable latent structures for high-dimensional data. Giventhe complexities of jointly training such a hybrid model, we introduce noveltheory that constrains linear ICA to lie close to the manifold of orthogonalrectangular matrices, the Stiefel manifold. By doing so we create models thatconverge quickly, are easy to train, and achieve better unsupervised latentfactor discovery than flow-based models, linear ICA, and VariationalAutoencoders on images.

Learning Bijective Feature Maps for Linear ICA