Causal Discovery From Bivariate Relationships
In Causal Discovery, we ask which models from a certain causal
(e.g., DAGs) would be consistent with a given dataset. Many causal discovery
algorithms are based on conditional independence testing. However, conditional
independence is difficult to test, especially when parametric assumptions like
normality cannot be made. Hence, we ask to what extent causal discovery is still
possible when we restrict our attention to only pairwise relationships, for
which a wide variety of both parametric and non-parametric statistical
independence tests are available. Suprisingly, we find that the entire class of
edge-maximal DAGs that are consistent with a given set of pairwise dependencies
can be described by a single graph, which can be constructed by a rather simple
algorithm. Furthermore, we give a precise characterization of how much
discrimination power we lose by not looking at conditional independencies.
Finally, we empirically investigate the failed discovery rate of the pairwise
approach -- assuming a correct DAG exists, how often is it rejected? -- and
compare the results to those the partial correlation based PC algorithm.