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arXiv 2102.03274cs.LGstat.AP
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因果发现的样本复杂性与领域专长的价值

On the Sample Complexity of Causal Discovery and the Value of Domain Expertise

University of Illinois(伊利诺伊大学)

Samir Wadhwa, Roy Dong

摘要:

因果发现方法试图从纯粹的观察数据中识别随机变量之间的因果关系,而不是主动收集实验数据,其中实验者干预相关性的子集。这一领域的开创性工作之一是推断因果关系算法,它保证在条件独立(CI)预言的假设下成功发现因果关系:一个预言可以说明两个随机变量是否在另一组随机变量下条件独立。该算法的实际实现包括条件独立性的统计测试,代替CI oracle。在本文中,我们分析了样本的复杂性,因果发现算法没有CI预言:给定一定程度的信心,有多少数据点是需要一个因果发现算法,以确定一个因果结构?此外,我们的方法使我们能够量化的数据样本方面的领域专业知识的价值。最后,我们用数值例子证明了这些采样率的准确性,并量化了稀疏先验和已知因果方向的好处。

英文摘要:

Causal discovery methods seek to identify causal relations between random variables from purely observational data, as opposed to actively collected experimental data where an experimenter intervenes on a subset of correlates. One of the seminal works in this area is the Inferred Causation algorithm, which guarantees successful causal discovery under the assumption of a conditional independence (CI) oracle: an oracle that can states whether two random variables are conditionally independent given another set of random variables. Practical implementations of this algorithm incorporate statistical tests for conditional independence, in place of a CI oracle. In this paper, we analyze the sample complexity of causal discovery algorithms without a CI oracle: given a certain level of confidence, how many data points are needed for a causal discovery algorithm to identify a causal structure? Furthermore, our methods allow us to quantify the value of domain expertise in terms of data samples. Finally, we demonstrate the accuracy of these sample rates with numerical examples, and quantify the benefits of sparsity priors and known causal directions.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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