  Causal discovery and causal effect estimation are two fundamental tasks in
causal inference. While many methods have been developed for each task
individually, statistical challenges arise when applying these methods jointly:
estimating causal effects after running causal discovery algorithms on the same
data leads to "double dipping," invalidating the coverage guarantees of
classical confidence intervals. To this end, we develop tools for valid
post-causal-discovery inference. Across empirical studies, we show that a naive
combination of causal discovery and subsequent inference algorithms leads to
highly inflated miscoverage rates; on the other hand, applying our method
provides reliable coverage while achieving more accurate causal discovery than
data splitting.
