Causal Inference: From Correlation to Causation

Module: Machine Learning | Difficulty: Advanced

Potential Outcomes

Rubin Causal Model

Fundamental problem: we observe only one potential outcome.

Do-Calculus (Pearl)

Instrumental Variables

Propensity Score

import numpy as np
from sklearn.linear_model import LogisticRegression

class IPW:
    def __init__(self):
        self.propensity = LogisticRegression()
    def fit(self, X, T):
        self.propensity.fit(X, T)
    def estimate_ATE(self, X, T, Y):
        e = self.propensity.predict_proba(X)[:, 1]
        e = np.clip(e, 0.01, 0.99)
        ate = np.mean(T * Y / e - (1-T) * Y / (1-e))
        return ate

Research Insight: Machine learning can estimate heterogeneous treatment effects (CATE) using methods like causal forests and meta-learners. The key challenge is that ML optimizes prediction, not causal estimation, leading to confounding bias.