This paper addresses intervention-based causal representation learning (CRL) under a general nonparametric latent causal model and an unknown transformation that maps the latent variables to the observed variables. Linear and general transformations are investigated. The paper addresses both the identifiability and achievability aspects. Identifiability refers to determining algorithm-agnostic conditions that ensure recovering the true latent causal variables and the latent causal graph underlying them. Achievability refers to the algorithmic aspects and addresses designing algorithms that achieve identifiability guarantees. By drawing novel connections between score functions (i.e., the gradients of the logarithm of density functions) and CRL, this paper designs a score-based class of algorithms that ensures both identifiability and achievability. First, the paper focuses on linear transformations and shows that one stochastic hard intervention per node suffices to guarantee identifiability. It also provides partial identifiability guarantees for soft interventions, including identifiability up to ancestors for general causal models and perfect latent graph recovery for sufficiently non-linear causal models. Secondly, it focuses on general transformations and shows that two stochastic hard interventions per node suffice for identifiability. Notably, one does not need to know which pair of interventional environments have the same node intervened.

翻译：本文研究了在一般非参数化潜在因果模型及将潜在变量映射至观测变量的未知变换下，基于干预的因果表示学习（CRL）。我们探讨了线性变换与一般变换两种情形，并同时解决了可辨识性与可实现性两方面问题。可辨识性指确定与算法无关的条件，以确保恢复真实的潜在因果变量及其背后的因果图；可实现性则涉及算法设计，旨在实现可辨识性保证。通过建立分数函数（即密度函数对数的梯度）与CRL之间的新颖联系，本文设计了一类基于分数的算法，同时确保可辨识性与可实现性。首先针对线性变换，我们证明每个节点进行一次随机硬干预即可保证可辨识性；对于软干预，我们提供了部分可辨识性保证，包括一般因果模型中基于祖先的辨识结果，以及充分非线性因果模型下潜在因果图的完整恢复。其次针对一般变换，我们证明每个节点进行两次随机硬干预即可实现可辨识性。值得注意的是，此方法无需事先知晓哪一对干预环境针对同一节点进行了干预。