Causal Inference

Causal inference is the process of determining the independent, actual effect of a particular phenomenon.

Key Concepts

Potential Outcomes Framework

For each unit $i$, we have potential outcomes:

• $Y_i(1)$: outcome if treated
• $Y_i(0)$: outcome if not treated

The Individual Treatment Effect is: ${\tau }_i=Y_i(1)-Y_i(0)$

The Average Treatment Effect is: $\text{ATE}=\mathbb{E}[Y(1)-Y(0)]$

Fundamental Problem of Causal Inference

We can never observe both $Y_i(1)$ and $Y_i(0)$ for the same unit!

Methods

1. Randomized Controlled Trials (RCTs) - Gold standard
2. Observational Studies - Require assumptions
3. Instrumental Variables
4. Regression Discontinuity

Connections

• Machine Learning methods can estimate heterogeneous treatment effects
• Important for Bioinformatics and drug discovery