Sensitivity analysis of violations of the faithfulness assumption

Abstract

We study the implication of violations of the faithfulness condition due to parameter cancellations on estimation of the directed acyclic graph (DAG) skeleton. Three settings are investigated: when (i) faithfulness is guaranteed (ii) faithfulness is not guaranteed and (iii) the parameter distributions are concentrated around unfaithfulness (near-unfaithfulness). In a simulation study, the effects of the different settings are compared using the parents and children (PC) and max–min parents and children (MMPC) algorithms. The results show that the performance in the faithful case is almost unchanged compared with the unrestricted case, whereas there is a general decrease in performance under the near-unfaithful case as compared with the unrestricted case. The response to near-unfaithful parameterizations is similar between the two algorithms, with the MMPC algorithm having higher true positive rates and the PC algorithm having lower false positive rates.