Empirical Bayesian Approaches for Robust Constraint-based Causal Discovery under Insufficient Data

TL;DR

This paper introduces Bayesian-augmented independence tests to enhance constraint-based causal discovery in scenarios with limited data, demonstrating improved accuracy and efficiency over state-of-the-art methods.

Contribution

It proposes novel Bayesian-augmented independence tests for causal discovery that are robust under insufficient data conditions, combining mutual information estimation and hypothesis likelihood.

Findings

Significant accuracy improvement over SOTA methods.

Enhanced efficiency in causal discovery tasks.

Robust performance with limited sample sizes.

Abstract

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.