Algorithm 1.

CBR-PC algorithm

Input: Observed dataset D with corresponding variable sets V,O,L,L*, and R; a known estimator g(D) of p(1R | V).

Output: An equivalence class of DAGs over V.

procedure CBR-PC

Construct an IPW-weighted conditional independence algorithm tester(A,B,C; D) for any ${(\mathbf{A}⫫\mathbf{B}|\mathbf{C})}_{p(\mathbf{Z})/p\left(1_{\mathbf{R}}|\mathbf{V}\right)}$ using D and g(D).

return PC-alg(D,tester(A,B,C;D)).

end procedure

⊳ PC-alg denotes the PC algorithm from Spirtes et al. (2001), taking as input a dataset D and an algorithm tester(.) for performing any conditional independence hypothesis test (A ⫫ B | C)p using a dataset D drawn from p.