Do we become wiser with time? On causal equivalence with tiered background knowledge
This work provides incremental improvements for researchers in causal inference by making equivalence classes more informative and computationally efficient through tiered background knowledge.
The paper addresses the problem that causal equivalence classes (CPDAGs) are often too large to provide useful causal information by introducing tiered background knowledge to create more informative restricted equivalence classes (tiered MPDAGs). This approach yields considerable gains in informativeness and computational efficiency, including requiring only Meek's 1st rule for construction, having chordal chain graph structures, and simplifying tasks like determining valid adjustment sets for causal effect estimation.
Equivalence classes of DAGs (represented by CPDAGs) may be too large to provide useful causal information. Here, we address incorporating tiered background knowledge yielding restricted equivalence classes represented by 'tiered MPDAGs'. Tiered knowledge leads to considerable gains in informativeness and computational efficiency: We show that construction of tiered MPDAGs only requires application of Meek's 1st rule, and that tiered MPDAGs (unlike general MPDAGs) are chain graphs with chordal components. This entails simplifications e.g. of determining valid adjustment sets for causal effect estimation. Further, we characterise when one tiered ordering is more informative than another, providing insights into useful aspects of background knowledge.