Algorithm 1 Structural Intervention Algorithm

Given a variable set $V$ with $n$ variables

Initialize the edge set: $E=\{ \}$

1.  Influence Discovery step:

for each $v_i$ in $V$

intervene on $v_i$

if the state of $v_j$ changes, where $j\ne i$,

add edge $v_i\to v_j$ to $E$

for each directed path $v_l\to v_{l+1}\to v_{l+2}\to \dots \to v_m$ in $E$

if there are any directed edges between $v_l\to v_{l+2}, \dots$

Goto 2

2.  Parent Confirmation step:

Simultaneously intervene on $v_l$ and $v_{l+1}$ by fixing $v_{l+1}$ and perturbing $v_l$

if the state of $v_{l+2}$ does not change

remove edge $v_l\to v_{l+2}$

return $G=\left(V,E\right)$