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.

翻译：将图像等高维数据分离成独立的潜伏因素,即独立组成部分分析(ICA),仍然是一个开放的研究问题。正如我们所显示的那样,现有的概率深重基因模型(DGMs)是针对图像数据而定制的,在非线性ICA任务方面表现不佳。为了解决这个问题,我们建议DGM将双向地貌图与线性ICA模型结合起来,以学习高维数据的可解释潜伏结构。鉴于联合培训这种混合模型的复杂性,我们引入了新颖理论,将线性ICA限制在接近正方形矩形矩阵(Stiefel 多重)的方形上。通过这样做,我们创建了快速聚合的模型,很容易进行培训,并且比流基模型、线性ICA和图像的动态自动解码更好地实现不受控制的潜在因素的发现。