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.

翻译：因果解耦旨在从数据中学习潜在的因果因子，有望在可解释性和外推性方面增强现有的表征学习方法。近期研究在假设能够对（单个）潜在因子进行干预的前提下建立了可辨识性结果；然而，由于干预潜在变量本身固有的性质，此类假设的合理性仍存争议。因此，我们重新审视基础问题，探讨仅利用观测数据能够学习到什么。我们针对具有加性高斯噪声和线性混合的非线性因果模型，在无需任何干预或图结构限制的条件下，精确刻画了可辨识的潜在因子特征。具体而言，我们证明了因果变量可被识别至层级变换的程度，且无法实现进一步的解耦。我们将这些理论结果转化为一种实用算法，该算法通过求解观测数据分数估计的二次规划问题实现。我们通过仿真结果验证了理论保证，并证明所提算法能够从纯观测数据中推导出有意义的因果表征。