Unsupervised representation learning with variational inference relies heavily on independence assumptions over latent variables. Causal representation learning (CRL), however, argues that factors of variation in a dataset are, in fact, causally related. Allowing latent variables to be correlated, as a consequence of causal relationships, is more realistic and generalisable. So far, provably identifiable methods rely on: auxiliary information, weak labels, and interventional or even counterfactual data. Inspired by causal discovery with functional causal models, we propose a fully unsupervised representation learning method that considers a data generation process with a latent additive noise model (ANM). We encourage the latent space to follow a causal ordering via loss function based on the Hessian of the latent distribution.

翻译：基于变分推断的无监督表示学习高度依赖潜变量之间的独立性假设。然而，因果表示学习（CRL）认为数据集中的变异因素实际上存在因果关系。允许潜变量因因果关系而相互关联更为真实且具有更好的泛化能力。迄今为止，可证明可识别的方法依赖于：辅助信息、弱标签、干预数据甚至反事实数据。受基于函数因果模型的因果发现启发，我们提出了一种完全无监督的表示学习方法，该方法考虑了具有潜在加性噪声模型（ANM）的数据生成过程。我们通过基于潜分布黑塞矩阵的损失函数，鼓励潜空间遵循因果序。