Conditional Independence Tests for Constraint-Based Causal Discovery: A Survey
2026-08-11 • Machine Learning
Machine Learning
AI summaryⓘ
The authors explain how tests that check if two things are independent given a third (called Conditional Independence tests) help figure out cause-and-effect relationships in data. They group popular test methods into six types and talk about when these methods work well or struggle, especially with complex biomedical data. They also connect mistakes in these tests to errors in the bigger cause-effect maps they help build. Finally, the authors review software tools and point out challenges like handling mixed data types and making tests work well with small or large datasets.
Conditional IndependenceCausal DiscoveryPC AlgorithmFCI AlgorithmPartial CorrelationKernel MethodsRegressionType I/II ErrorsHigh-dimensional DataMixed-type Data
Authors
Pavel Averin, Theodoros Moysiadis, Ioannis Katakis
Abstract
Conditional Independence (CI) tests are the statistical engine of constraint-based causal discovery: in algorithms such as PC (Peter-Clark) and FCI (Fast Causal Inference), skeleton pruning and key orientations follow directly from CI decisions. This survey reviews CI testing with emphasis on assumptions, robustness, and scalability in high-dimensional and mixed-type settings common in biomedical domains. The survey organizes widely used CI methods into six families: partial-correlation, contingency-table, regression, nearest-neighbor, kernel, and machine-learning-based. Special emphasis is provided on the robustness layers that address the limitations of these families. For each family, the survey examines when CI decisions reflect the data-generating distribution and when they fail. By this, we link test-level properties, including power decay with conditioning set size and asymmetric type I/II error consequences, to graph-level errors in skeleton recovery and v-structure orientation. The survey also compares adoption across major R and Python libraries and summarizes open challenges, including mixed-type CI testing without discretization, small-sample error control, and strategies for improving scalability of CI-testing.