Learning Bijective Feature Maps for Linear ICA

TL;DR

This paper introduces a hybrid deep generative model combining bijective feature maps with linear ICA to improve unsupervised latent factor discovery in high-dimensional data like images, addressing limitations of existing models.

Contribution

It proposes a novel DGM that integrates bijective feature maps with linear ICA and introduces theory to constrain ICA to the Stiefel manifold, enabling better training and interpretability.

Findings

Achieves superior latent factor discovery compared to flow-based models, ICA, and VAEs.

Models converge quickly and are easier to train.

Effective on high-dimensional image data.

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.