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Abstract:
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We consider causal structure learning from high-dimensional observational data. The main approaches can be classified as constraint-based, score-based or hybrid methods. Although high-dimensional consistency results are available for constraint-based methods like the PC algorithm, such results have not been proved for score-based or hybrid methods, and most of the hybrid methods are not even proved to be consistent in the classical setting where the number of variables remains fixed and the sample size tends to infinity. We show that consistency of hybrid methods based on greedy equivalence search (GES) can be achieved in the classical setting with adaptive restrictions on the search space that depend on the current state of the algorithm. Moreover, we prove consistency of GES and adaptively restricted GES (ARGES) in certain sparse high-dimensional settings (where the number of variables is allowed to grow with the sample size). In simulation studies, we found that ARGES combines the best aspects of the constraint-based PC algorithm and the score-based GES algorithm: the fast computation of PC and the good estimation performance of GES.
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