Nonlinear independent component analysis (ICA) aims to recover the underlying independent latent sources from their observable nonlinear mixtures. How to make the nonlinear ICA model identifiable up to certain trivial indeterminacies is a long-standing problem in unsupervised learning. Recent breakthroughs reformulate the standard independence assumption of sources as conditional independence given some auxiliary variables (e.g., class labels and/or domain/time indexes) as weak supervision or inductive bias. However, nonlinear ICA with unconditional priors cannot benefit from such developments. We explore an alternative path and consider only assumptions on the mixing process, such as Structural Sparsity. We show that under specific instantiations of such constraints, the independent latent sources can be identified from their nonlinear mixtures up to a permutation and a component-wise transformation, thus achieving nontrivial identifiability of nonlinear ICA without auxiliary variables. We provide estimation methods and validate the theoretical results experimentally. The results on image data suggest that our conditions may hold in a number of practical data generating processes.
翻译:非线性独立部件分析(ICA)旨在从可观测的非线性非线性混合物中回收潜在的潜在源。如何使非线性ICA模型可识别到某些微不足道的不确定性是一个长期的问题。最近的突破将源的标准独立假设重新确定为有条件的独立,因为一些辅助变量(如类标签和/或域/时间指数)是薄弱的监督或感应偏差。然而,具有无条件前科的非线性ICA不能从这种发展中受益。我们探索了一条替代路径,只考虑混合过程的假设,例如结构平衡。我们表明,在这种制约的具体即时反应下,可以从非线性混合物中找出独立的潜在来源,直至一个整变和部分的转化,从而在没有辅助变量的情况下实现非线性非线性ICA的可识别性。我们提供了估算方法,并以实验方式验证了理论结果。图像数据的结果表明,我们的条件可能存在于一些实际的数据生成过程中。