Causal discovery is to learn cause-effect relationships among variables given observational data and is important for many applications. Existing causal discovery methods assume data sufficiency, which may not be the case in many real world datasets. As a result, many existing causal discovery methods can fail under limited data. In this work, we propose Bayesian-augmented frequentist independence tests to improve the performance of constraint-based causal discovery methods under insufficient data: 1) We firstly introduce a Bayesian method to estimate mutual information (MI), based on which we propose a robust MI based independence test; 2) Secondly, we consider the Bayesian estimation of hypothesis likelihood and incorporate it into a well-defined statistical test, resulting in a robust statistical testing based independence test. We apply proposed independence tests to constraint-based causal discovery methods and evaluate the performance on benchmark datasets with insufficient samples. Experiments show significant performance improvement in terms of both accuracy and efficiency over SOTA methods.

通过引入贝叶斯-augmented的频率独立性检验方法，可以解决数据量不足的问题来改善局限于有限数据的约束性因果发现方法的性能，由实验也表明相比于目前最佳方法在精确度和效率方面都有显著提高。

基于经验贝叶斯方法的鲁棒性基于约束因果发现在不充足数据下的应用