Front-door Adjustment Beyond Markov Equivalence with Limited Graph
  Knowledge
Abhin Shah Karthikeyan Shanmugam Murat Kocaoglu
Causal effect estimation from data typically requires assumptions about the
cause-effect relations either explicitly in the form of a causal graph
structure within the Pearlian framework, or implicitly in terms of
(conditional) independence statements between counterfactual variables within
the potential outcomes framework. When the treatment variable and the outcome
variable are confounded, front-door adjustment is an important special case
where, given the graph, causal effect of the treatment on the target can be
estimated using post-treatment variables. However, the exact formula for
front-door adjustment depends on the structure of the graph, which is difficult
to learn in practice. In this work, we provide testable conditional
independence statements to compute the causal effect using front-door-like
adjustment without knowing the graph under limited structural side information.
We show that our method is applicable in scenarios where knowing the Markov
equivalence class is not sufficient for causal effect estimation. We
demonstrate the effectiveness of our method on a class of random graphs as well
as real causal fairness benchmarks.