在未知干预下学习非参数隐变量因果图
Learning nonparametric latent causal graphs with unknown interventions
AI总结：
该研究确立了无参数假设、隐变量数量未知且存在未知干预的通用设定下，隐变量因果图的非参数可识别条件，引入全新图论概念完成构造性证明，首次刻画了无忠实性假设下因果表征的可识别性。
摘要：
我们确立了隐变量因果图可非参数识别、且能从隐空间中的未知干预中重建的条件。本研究核心聚焦于测量模型中的隐结构识别，无需做出线性或高斯性等参数假设。此外，我们并未假设隐变量数量已知，且证明每个隐变量最多仅需一次未知干预即可实现识别，这拓展了近期从观测与干预中学习因果表征的一系列研究。相关证明是构造性的，同时引入了两个全新的图论概念——虚子集（imaginary subsets）与孤立边（isolated edges），二者本身也具备研究价值。作为具有独立研究意义的内容，证明过程还对未知干预所诱导的有向无环图（DAG）等价类中边定向的极限给出了全新刻画。这是首批在无参数假设、存在未知干预且不满足忠实性的通用设定下，刻画因果表征可识别性条件的研究成果。
英文摘要：
We establish conditions under which latent causal graphs are nonparametrically identifiable and can be reconstructed from unknown interventions in the latent space. Our primary focus is the identification of the latent structure in measurement models without parametric assumptions such as linearity or Gaussianity. Moreover, we do not assume the number of hidden variables is known, and we show that at most one unknown intervention per hidden variable is needed. This extends a recent line of work on learning causal representations from observations and interventions. The proofs are constructive and introduce two new graphical concepts -- imaginary subsets and isolated edges -- that may be useful in their own right. As a matter of independent interest, the proofs also involve a novel characterization of the limits of edge orientations within the equivalence class of DAGs induced by unknown interventions. These are the first results to characterize the conditions under which causal representations are identifiable without making any parametric assumptions in a general setting with unknown interventions and without faithfulness.
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