Many constraint-based algorithms for causal discovery have suffered from statistical errors in conditional independence (CI) tests. Those errors are often inevitable in real data because of the limitation of statistical power due to finiteness of data or violations of an assumption called faithfulness or stability con- dition. We propose a constraint-based algorithm that can reduce avoidable CI tests with combining an adjacency identification stage with an orientation stage and then provide accurate and fast inference without loss of theoretical correctness, which we call the Combining Stage (CS) algorithm. We also, in the algorithm, introduce unreliable direction, which can reduce orientation errors due to locality of CI tests. Simulations are provided to demonstrate the prominent performance of the algorithm by comparison it to often referred algorithms: PC, Three Phase Dependency Analysis, Sparse Candidate, and Max-Min Hill-Climbing algorithms.

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