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Conditional independence (CI) testing is frequently used in data analysis andmachine learning for various scientific fields and it forms the basis ofconstraint-based causal discovery. Oftentimes, CI testing relies on strong,rather unrealistic assumptions. One of these assumptions is homoskedasticity,in other words, a constant conditional variance is assumed. We frameheteroskedasticity in a structural causal model framework and present anadaptation of the partial correlation CI test that works well in the presenceof heteroskedastic noise, given that expert knowledge about the heteroskedasticrelationships is available. Further, we provide theoretical consistency resultsfor the proposed CI test which carry over to causal discovery under certainassumptions. Numerical causal discovery experiments demonstrate that theadapted partial correlation CI test outperforms the standard test in thepresence of heteroskedasticity and is on par for the homoskedastic case.Finally, we discuss the general challenges and limits as to how expertknowledge about heteroskedasticity can be accounted for in causal discovery.

Conditional Independence Testing with Heteroskedastic Data and Applications to Causal Discovery