未知干预下因果表示的非参数可辨识性
Nonparametric Identifiability of Causal Representations from Unknown Interventions
AI总结：
本文研究未知干预下非参数因果表示学习的可辨识性，证明在一般性条件下，每个节点一次完美干预即可识别两个因果变量，并推广到任意数量变量，同时证明因果影响强度在等价解中保持不变。
摘要：
我们研究因果表示学习，即从高维变量混合中推断潜在因果变量及其因果关系的任务。先前的工作依赖于弱监督，例如反事实的干预前后视图或时间结构；对混合函数或潜在因果模型施加线性等限制性假设；或者要求对生成过程有部分了解，例如因果图或干预目标。我们转而考虑因果模型和混合函数均为非参数的一般设定。学习信号以多个数据集或环境的形式出现，这些数据集或环境来自底层因果模型中的未知干预。我们的目标是识别真实的潜在变量及其因果图，直至一组我们证明无法从干预数据中消除的歧义。我们研究两个因果变量的基本设定，并证明在满足一般性条件的前提下，观测分布和每个节点一次完美干预足以实现可辨识性。该条件排除了涉及对干预分布和观测分布进行精细调节的虚假解，这与非线性因果推断中的类似条件相呼应。对于任意数量的变量，我们证明每个节点至少有一对不同的完美干预域即可保证可辨识性。此外，我们证明潜在变量之间因果影响的强度在所有等价解中均得以保留，从而使推断出的表示适用于从新数据中得出因果结论。我们的研究为具有未知干预的一般非参数设定提供了首个可辨识性结果，并阐明了在没有更直接监督的情况下因果表示学习可能实现与不可能实现的目标。
英文摘要：
We study causal representation learning, the task of inferring latent causal variables and their causal relations from high-dimensional 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 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 at least one pair of distinct perfect interventional domains per node guarantees 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.
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