Book - Causal Inference for The Brave and True

Summary: Causal Inference for The Brave and True

Terminology

n: # of subjects or observations, where i is one suject

$T_i$: Treatment

$Y_i$: Response

$X_i$: Feature Vector

• Potential Outcomes: $Y_i(1)$ and $Y_i(0)$

• Actual Outcome: $Y_i$

• Causal Effect = $Y_i(1)-Y_i(0)$

• Avg. Treatment Effect (ATE) = $E[Y_i(1)-Y_i(0)]$

• Conditional Avg. Treatment Effect (CATE) = $E[Y_i(1)-Y_i(0) \ | \ X_i=x]$

Need for causal analysis

ATE Calculations

• We only have one actual outcome, so can’t get the value of both potential outcomes
• So, we have a problem of missing counterfactuals