Practical on DAGs, bonus exercises

1 Causal Factorization

Take this DAG

Figure 1: DAG

TipWrite down the causal factorization of the joint distribution over \(Y,T,Z,W\) for this DAG

answer:

• \(P(Y,T,Z,W) = P(Y|T,Z)P(T|Z,W)P(Z)P(W)\)

TipDraw the mutilated DAG after intervening on \(T\)

answer:

Figure 2: mutilated DAG

TipWrite down the factorization for the joint in the mutilated DAG after intervening on \(T\)

answer:

Figure 3: mutilated DAG

• \(P(Y,T,Z,W) = P(Y|T,Z)P(T)P(Z)P(W)\)