Do we become wiser with time? On causal equivalence with tiered background knowledge

Christine W. Bang, Vanessa Didelez

Keywords: causal discovery, causal graphs, graphical models, Markov equivalence, temporal structure

TL;DR: We show formally why and when incorporating tiered background knowledge into equivalence classes of DAGs leads to considerable gains in informativeness and computational efficiency.

Abstract: 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.