Automated hyperparameter selection for the PC algorithm

Abstract

• The performance of the PC algorithm depends heavily on the choice of the Type I error rate α . • We propose to automatically tune α for a user chosen metric using a procedure called AutoPC. • AutoPC double checks the output of PC by rerunning the algorithm on restricting conditioning sets. • AutoPC provably maximizes the chosen metric and recovers the true CPDAG in the sample limit. • The algorithm also easily achieves state-of-the-art accuracy across multiple metrics with both synthetic and real data. The PC algorithm infers causal relations using conditional independence tests that require a pre-specified Type I α level. PC is however unsupervised, so we cannot tune α using traditional cross-validation. We therefore propose AutoPC, a fast procedure that optimizes α directly for a user chosen metric. We in particular force PC to double check its output by executing a second run on the recovered graph. We choose the final output as the one which maximizes stability between the two runs. AutoPC consistently outperforms the state of the art across multiple metrics.