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

TL;DR

This paper introduces tiered MPDAGs, a new class of causal graph representations that incorporate tiered background knowledge, improving informativeness and computational efficiency in causal inference tasks.

Contribution

It proposes tiered MPDAGs as a restricted class of causal graphs, demonstrating their construction, properties, and advantages over general MPDAGs.

Findings

Tiered MPDAGs are chain graphs with chordal components.

Construction of tiered MPDAGs only requires Meek's 1st rule.

Tiered MPDAGs improve causal effect estimation and background knowledge utilization.

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.