We study causal representation learning, the task of inferring latent causal variables and their causal relations from high-dimensional functions ("mixtures") of the variables. Prior work relies on weak supervision, in the form of counterfactual pre- and post-intervention views or temporal structure; places restrictive assumptions, such as linearity, on the mixing function or latent causal model; or requires partial knowledge of the generative process, such as the causal graph or the intervention targets. We instead consider the general setting in which both the causal model and the mixing function are nonparametric. The learning signal takes the form of multiple datasets, or environments, arising from unknown interventions in the underlying causal model. Our goal is to identify both the ground truth latents and their causal graph up to a set of ambiguities which we show to be irresolvable from interventional data. We study the fundamental setting of two causal variables and prove that the observational distribution and one perfect intervention per node suffice for identifiability, subject to a genericity condition. This condition rules out spurious solutions that involve fine-tuning of the intervened and observational distributions, mirroring similar conditions for nonlinear cause-effect inference. For an arbitrary number of variables, we show that two distinct paired perfect interventions per node guarantee identifiability. Further, we demonstrate that the strengths of causal influences among the latent variables are preserved by all equivalent solutions, rendering the inferred representation appropriate for drawing causal conclusions from new data. Our study provides the first identifiability results for the general nonparametric setting with unknown interventions, and elucidates what is possible and impossible for causal representation learning without more direct supervision.

翻译：我们研究因果表示学习，即从变量的高维函数（“混合”）中推断潜在因果变量及其因果关系的任务。先前的工作依赖弱监督（以反事实干预前后视图或时间结构的形式）、施加限制性假设（如混合函数或潜在因果模型的线性性）、或需要生成过程的局部知识（如因果图或干预目标）。我们则考虑因果模型和混合函数均为非参数的通用设置。学习信号以多数据集（或多环境）的形式出现，这些数据集源自底层因果模型中的未知干预。我们的目标是识别真实潜在变量及其因果图，但需考虑一组我们证明无法从干预数据中消除的歧义。我们研究了两个因果变量的基本设置，并证明在一般性条件下，观察分布与每个节点的一次完美干预足以保证可辨识性。该条件排除了涉及干预分布与观察分布精细调整的虚假解，类似于非线性因果效应推断中的类似条件。对于任意数量的变量，我们证明每个节点两次不同的配对完美干预可确保可辨识性。此外，我们展示所有等价解均保留潜在变量间因果影响的强度，使得推断表示适用于从新数据中得出因果结论。本研究首次为具有未知干预的通用非参数设置提供了可辨识性结果，并阐明了在缺乏更直接监督的情况下因果表示学习可能实现与无法实现的内容。