  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.
