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Learning causal structure is useful in many areas of artificial intelligence,including planning, robotics, and explanation. Constraint-based structurelearning algorithms such as PC use conditional independence (CI) tests to infercausal structure. Traditionally, constraint-based algorithms perform CI testswith a preference for smaller-sized conditioning sets, partially because thestatistical power of conventional CI tests declines rapidly as the size of theconditioning set increases. However, many modern conditional independence testsare model-based, and these tests use well-regularized models that maintainstatistical power even with very large conditioning sets. This suggests anintriguing new strategy for constraint-based algorithms which may result in areduction of the total number of CI tests performed: Test variable pairs withlarge conditioning sets first, as a pre-processing step that finds someconditional independencies quickly, before moving on to the more conventionalstrategy that favors small conditioning sets. We propose such a pre-processingstep for the PC algorithm which relies on performing CI tests on a few randomlyselected large conditioning sets. We perform an empirical analysis on directedacyclic graphs (DAGs) that correspond to real-world systems and both empiricaland theoretical analyses for Erd\H{o}s-Renyi DAGs. Our results show thatPre-Processing Plus PC (P3PC) performs far fewer CI tests than the original PCalgorithm, between 0.5% to 36%, and often less than 10%, of the CI tests thatthe PC algorithm alone performs. The efficiency gains are particularlysignificant for the DAGs corresponding to real-world systems.

Improving the Efficiency of the PC Algorithm by Using Model-Based Conditional Independence Tests