Johannes Textor
Causal Discovery From Bivariate Relationships
In Causal Discovery, we ask which models from a certain causal
model class
(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.