Causal Discovery from Soft Interventions with Unknown Targets: Characterization and Learning
Causal Discovery from Soft Interventions with Unknown Targets: Characterization and Learning
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发表时间：
2020
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通讯作者：
Amin Jaber;Murat Kocaoglu
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作者：
Amin Jaber;Murat Kocaoglu
经验科学中的一个基本问题是通过观察和实验来重建作为感兴趣现象基础的因果结构。虽然存在大量能够学习与观察相容的因果结构的等价类的方法，但如何系统地将观察和实验联合收割机组合以重构底层结构还不太清楚。在本文中，我们研究了非马尔可夫系统（即，当潜在变量是一个以上的可观测值时），当介入目标是未知的时，从观测数据和软实验数据的组合。使用在观察和干预分布的集合中发现的因果不变性（不仅是条件独立性），我们定义了一个称为马尔可夫的属性，该属性将这些分布连接到由（1）因果图D和（2）一组干预目标I组成的对。建立在这个属性，我们的主要贡献是双重的：首先，我们提供了一个图形表征，允许一个测试是否有可能不同的干预目标集的两个因果图属于同一个马尔可夫等价类。其次，我们开发了一种算法，能够利用收集的数据来学习相应的等价类。然后，我们证明，这个算法是健全的和完整的，在这个意义上，它是最翔实的样本限制，即，它发现尽可能多的尾巴和箭头，因为可以在一个马尔可夫等价类中定向。
One fundamental problem in the empirical sciences is of reconstructing the causal structure that underlies a phenomenon of interest through observation and experimentation. While there exists a plethora of methods capable of learning the equivalence class of causal structures that are compatible with observations, it is less well-understood how to systematically combine observations and experiments to reconstruct the underlying structure. In this paper, we investigate the task of structural learning in non-Markovian systems (i.e., when latent variables a ff ect more than one observable) from a combination of observational and soft experimental data when the interventional targets are unknown. Using causal invariances found across the collection of observational and interventional distributions (not only conditional independences), we define a property called Ψ -Markov that connects these distributions to a pair consisting of (1) a causal graph D and (2) a set of interventional targets I . Building on this property, our main contributions are two-fold: First, we provide a graphical characterization that allows one to test whether two causal graphs with possibly di ff erent sets of interventional targets belong to the same Ψ -Markov equivalence class. Second, we develop an algorithm capable of harnessing the collection of data to learn the corresponding equivalence class. We then prove that this algorithm is sound and complete, in the sense that it is the most informative in the sample limit, i.e., it discovers as many tails and arrowheads as can be oriented within a Ψ -Markov equivalence class.