Double Machine Learning (DML) for Causal Inference

🤖 Double Machine Learning (DML)

Double Machine Learning (DML) uses flexible machine learning models to estimate nuisance parameters (e.g., propensity scores, outcome models) and removes their bias via orthogonalization, enabling valid causal inference.

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1. 🧪 Simulate Data with Confounding

set.seed(123)
n <- 1000

X1 <- rnorm(n)
X2 <- rnorm(n)
W <- rbinom(n, 1, prob = plogis(0.5 * X1 + 0.5 * X2))
Y <- 2 * W + 1.5 * X1 + 1.0 * X2 + rnorm(n)

df <- data.frame(X1, X2, W, Y)

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2. 🔍 DML Steps

(a) Split into folds

folds <- createFolds(df$Y, k = 2)
train1 <- df[folds[[1]], ]
train2 <- df[folds[[2]], ]

(b) Estimate nuisance functions

# Outcome model: Y ~ X1 + X2 (train2 on train1)
y_model <- cv.glmnet(as.matrix(train1[, c("X1", "X2")]), train1$Y)
m_Y2 <- predict(y_model, as.matrix(train2[, c("X1", "X2")]), s = "lambda.min")

# Treatment model: W ~ X1 + X2
w_model <- cv.glmnet(as.matrix(train1[, c("X1", "X2")]), train1$W, family = "binomial")
m_W2 <- predict(w_model, as.matrix(train2[, c("X1", "X2")]), s = "lambda.min", type = "response")

(c) Orthogonalization

res_Y <- train2$Y - m_Y2
res_W <- train2$W - m_W2

alpha_hat <- coef(lm(res_Y ~ res_W))[2]
cat("Estimated Treatment Effect (DML):", round(alpha_hat, 3))

## Estimated Treatment Effect (DML): 1.983

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✅ Summary

Double Machine Learning: - Uses ML to estimate nuisance models (Y|X and W|X) - Debiases via residual-on-residual regression - Yields valid causal estimates with flexible modeling

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📖 References

• Chernozhukov et al. (2018). Double/Debiased Machine Learning for Treatment and Structural Parameters
• Athey & Imbens (2019). Machine Learning and Econometrics