Causal disentanglement aims to learn about latent causal factors behind data, holding the promise to augment existing representation learning methods in terms of interpretability and extrapolation. Recent advances establish identifiability results assuming that interventions on (single) latent factors are available; however, it remains debatable whether such assumptions are reasonable due to the inherent nature of intervening on latent variables. Accordingly, we reconsider the fundamentals and ask what can be learned using just observational data. We provide a precise characterization of latent factors that can be identified in nonlinear causal models with additive Gaussian noise and linear mixing, without any interventions or graphical restrictions. In particular, we show that the causal variables can be identified up to a layer-wise transformation and that further disentanglement is not possible. We transform these theoretical results into a practical algorithm consisting of solving a quadratic program over the score estimation of the observed data. We provide simulation results to support our theoretical guarantees and demonstrate that our algorithm can derive meaningful causal representations from purely observational data.

本研究解决了因果解缠中的一个关键问题，即如何仅凭观测数据识别潜在因果因素。作者提出了一种新的方法，通过在非线性因果模型中对潜在变量进行精确表征，不需要进行干预。这一理论成果转化为实用算法，并通过模拟结果验证，其在仅使用观测数据时能够生成有意义的因果表示。

基于纯观测数据的因果解缠理论可识别性保证