The causal revolution has spurred interest in understanding complex
relationships in various fields. Most existing methods aim to discover causal
relationships among all variables in a large-scale complex graph. However, in
practice, only a small number of variables in the graph are relevant for the
outcomes of interest. As a result, causal estimation with the full causal graph
-- especially given limited data -- could lead to many falsely discovered,
spurious variables that may be highly correlated with but have no causal impact
on the target outcome. In this paper, we propose to learn a class of necessary
and sufficient causal graphs (NSCG) that only contains causally relevant
variables for an outcome of interest, which we term causal features. The key
idea is to utilize probabilities of causation to systematically evaluate the
importance of features in the causal graph, allowing us to identify a subgraph
that is relevant to the outcome of interest. To learn NSCG from data, we
develop a score-based necessary and sufficient causal structural learning
(NSCSL) algorithm, by establishing theoretical relationships between
probabilities of causation and causal effects of features. Across empirical
studies of simulated and real data, we show that the proposed NSCSL algorithm
outperforms existing algorithms and can reveal important yeast genes for target
heritable traits of interest.

本文提出了一种能学习到只包含和我们感兴趣的结果相关的因果相关变量的必要和充分因果图（NSCG）的方法，该方法使用了因果关系的概率。我们开发了一个基于分数的算法来学习 NSCG，并在模拟和真实数据的实证研究中展示了该算法的性能优于现有算法，并能揭示对于目标可遗传特征非常重要的酵母基因。