Causal Machine Learning

• Motivating Questions
• Key Terminology
• Treatment Effects
• Do-operator
• Assumptions of Causal Learning

Motivating Questions

• Causal machine learning asks, “What would happen if we took another action in the past?”
• Different past actions can lead to causal inference - if I changed this action and the outcome is different, then that action is a cause

Key Terminology

• Confounder: A variable that affects multiple parts of a model
  • $C \rightarrow (A, Y), C \rightarrow A \text{, so C is a confounder}$
• Mediator: A variable that is downstream of A but upstream of Y
  • $A \rightarrow M \rightarrow Y$

Treatment Effects

• Measures how much changing a past action affects the result
• Indirect Effect: How much one variable affects another through mediators

  • $IE = E(Y

    do(A = a, M = m_{a+1})) - E(Y

    do(A = a))$

• Direct Effect: How much one variable affects another, directly

  • $DE = E(Y

    do(A = a+1, M = m_{a})) - E(Y

    do(A = a))$

• Total Effect: How much one variable effects another, totally

  • $TE = IE + DE = E(Y

    do(A=a+1)) - E(Y

    do(A=a))$

• Heterogenous Treatment Effect

  • $HTE = E(Y^(1) - Y^(0)

    X) = E(Y

    A=1, X) - E(Y

    A=0, X)$

• Average Treatment Effect

  • $ATE = E(Y(1) - Y(0)) = E(Y

    do(A=1)) - E(Y

    do(A=0))$

• Individualized Treatment Effect
  • $ITE = Y_i - Y_i^* (0) \text{, given that subject i was assigned treatment 1}$

Do-operator

• Do-operator: denotes the intervention of treatment; that is, changing A = a_i to A = a_j while holding everything else constant
• Can be used to learn a policy π and see the effects: $Y^*(A = \pi (x))$
• Do-operator notations

  • $Y(a) \triangleq Y^*(a) \triangleq Y

    do(A = a) \triangleq Y_{do(A=a)}$

Assumptions of Causal Learning

• Stable Unit Treatment Value Assumption (SUTVA): $Y = Y^* (a)$

• No Unmeasured Cofounders: ${Y^* (a) : a \in A} \perp A

  X$

  • Allows us to find the true causal graph