do-calculus

Interventions and counterfactuals are represented by do(x), which simulate the physical interventions by deleting certain functions from the model and replacing them with constant (X=x), while keeping the rest of the model unchanged.

When we intervene on a variable, we have a constant variable for the treatment

With observational data, we can build the causal Graph on the left-hand side and to better understand the causal relationships we do an intervention on X and observe the effects of the intervention. The right graph helps us answer what would happen if we do an intervention

Interventions:

Graphical Representaion of Intervention

In the figure above,

$$Left: Title\:Length \leftarrow Author's\: Skill \\ Right: Title\:Length \leftarrow Yes(Constant)$$

Interventional Distritution:

$$P(CTR, Authors Skill \:| \: do(X=Yes)$$