Insensitivity of Constraint-Based Causal Discovery Algorithms to Violations of the Assumption of Multivariate Normality

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Constraint-based causal discovery algorithms, such as the PC algorithm, rely on conditional independence tests and are otherwise independent of the actual distribution of the data. In case of continuous variables, the most popular conditional independence test used in practice is the partial correlation test, applicable to variables that are multivariate Normal. Many researchers assume multivariate Normal distributions when dealing with continuous variables, based on a common wisdom that minor departures from multivariate Normality do not have a too strong effect on the reliability of partial correlation tests. We subject this common wisdom to a test in the context of causal discovery and show that partial correlation tests are indeed quite insensitive to departures from multivariate Normality. They, therefore, provide conditional independence tests that are applicable to a wide range of multivariate continuous distributions.