  Even when the causal graph underlying our data is unknown, we can use
observational data to narrow down the possible values that an average treatment
effect (ATE) can take by (1) identifying the graph up to a Markov equivalence
class; and (2) estimating that ATE for each graph in the class. While the PC
algorithm can identify this class under strong faithfulness assumptions, it can
be computationally prohibitive. Fortunately, only the local graph structure
around the treatment is required to identify the set of possible ATE values, a
fact exploited by local discovery algorithms to improve computational
efficiency. In this paper, we introduce Local Discovery using Eager Collider
Checks (LDECC), a new local causal discovery algorithm that leverages
unshielded colliders to orient the treatment's parents differently from
existing methods. We show that there exist graphs where LDECC exponentially
outperforms existing local discovery algorithms and vice versa. Moreover, we
show that LDECC and existing algorithms rely on different faithfulness
assumptions, leveraging this insight to weaken the assumptions for identifying
the set of possible ATE values.
