University of Michigan - Ann Arbor

When deconfounding $X$ and $Y$, a back-door path is any path from $X$ to $Y$ that starts with an arrow pointing into $X$. (Notice that if there is a collider on the back-door path, the path is already blocked by the collider.)

The path A <- B <- C -> D -> E is a back-door path for A to E. Forks are also back-door paths.

Back-door path

Pearl, J., & Mackenzie, D. (2018). $\mathit{The \ Book \ of \ Why: \ The \ New \ Science \ of \ Cause \ and \ Effect.}$ Basic Books.

The Book of Why

In the following causal diagram, which of the following are confounding back-door paths for A to F?

For Causal Nodes X,Y:
X and Y will be deconfounded if we block every backdoor, because such paths allow for spurious correlations. 

When eliminating backdoors, we additionally need to ensure that anything closed off from X is not a descendent of X.

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