We examine the performance of some standard causal discovery algorithms, both constraint-based and score-based, from the perspective of how robust they are against failures of the Causal Faithfulness Assumption. For this purpose, we make only the so-called Triangle-Faithfulness assumption, which is a fairly weak consequence of the Faithfulness assumption, and otherwise allows unfaithful distributions. In particular, we allow violations of Adjacency-Faithfulness and Orientation-Faithfulness. We show that the PC algorithm, a representative constraint-based method, can be made more robust against unfaithfulness by (...) incorporating elements of the GES algorithm, a representative score-based method; similarly, the GES algorithm can be made less error-prone by incorporating elements of the conservative PC algorithm. As our simulations demonstrate, the increased robustness seems to matter even when faithfulness is not exactly violated, for with only finite sample, distributions that are not exactly unfaithful may be sufficiently close to being unfaithful to make trouble. (shrink)

Using the flexibility of recently developed methods for causal discovery based on Boolean satisfiability solvers, we encode a variety of assumptions that weaken the Faithfulness assumption. The encoding results in a number of SAT-based algorithms whose asymptotic correctness relies on weaker conditions than are standardly assumed. This implementation of a whole set of assumptions in the same platform enables us to systematically explore the effect of weakening the Faithfulness assumption on causal discovery. An important effect, suggested by simulation results, is (...) that adopting weaker assumptions greatly alleviates the problem of conflicting constraints and substantially shortens solving time. As a result, SAT-based causal discovery is potentially more scalable under weaker assumptions. (shrink)