Learning Bijective Feature Maps for Linear ICA
This addresses the challenge of interpretable latent structure discovery in high-dimensional data for researchers in machine learning, though it appears incremental as it builds on existing models with novel constraints.
The paper tackles the problem of separating high-dimensional data like images into independent latent factors for linear ICA, proposing a deep generative model that combines bijective feature maps with linear ICA to achieve better unsupervised latent factor discovery than existing methods, with improved convergence and ease of training.
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.