有向树的结构学习
Structure Learning for Directed Trees
摘要：
了解系统的因果结构是许多科学领域的基本兴趣，并且可以帮助设计在系统操纵下工作良好的预测算法。在一定的限制条件下，因果结构可以从观测分布中识别出来。为了从数据中学习结构，基于分数的方法根据拟合的质量来评估不同的图。然而，对于大型的、连续的和非线性的模型，这些依赖于启发式优化方法，不能保证恢复真正的因果结构。本文研究有向树的结构学习。我们提出了一个快速和可扩展的方法的基础上，Chu-Liu-Edmonds的算法，我们称之为因果加性树（CAT）。对于高斯误差的情况，我们证明了可识别性差距消失的渐进状态下的一致性。我们还介绍了两种方法来测试子结构假设与渐近族明智的错误率控制，是有效的后选择，并在身份不明的设置。此外，我们研究了可识别性差距，它量化了真实因果模型与观测分布的拟合程度，并证明了它是由因果模型的局部性质下界。仿真研究表明，CAT的良好性能相比，竞争的结构学习方法。
英文摘要：
Knowing the causal structure of a system is of fundamental interest in many areas of science and can aid the design of prediction algorithms that work well under manipulations to the system. The causal structure becomes identifiable from the observational distribution under certain restrictions. To learn the structure from data, score-based methods evaluate different graphs according to the quality of their fits. However, for large, continuous, and nonlinear models, these rely on heuristic optimization approaches with no general guarantees of recovering the true causal structure. In this paper, we consider structure learning of directed trees. We propose a fast and scalable method based on Chu-Liu-Edmonds' algorithm we call causal additive trees (CAT). For the case of Gaussian errors, we prove consistency in an asymptotic regime with a vanishing identifiability gap. We also introduce two methods for testing substructure hypotheses with asymptotic family-wise error rate control that is valid post-selection and in unidentified settings. Furthermore, we study the identifiability gap, which quantifies how much better the true causal model fits the observational distribution, and prove that it is lower bounded by local properties of the causal model. Simulation studies demonstrate the favorable performance of CAT compared to competing structure learning methods.
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