Meta-Learners: S- vs T- vs X-Learner

Meta-Learners for CATE Estimation (S-Learner, T-Learner, X-Learner & R-Learner, Künzel et al. & Nie et al.) formulate causal inference algorithms leveraging any standard regression model (LightGBM, XGBoost, Deep Nets) as base estimators; 1) S-Learner (Single Model): pooling treatment indicator $T$ as a standard feature into one model $\mu(X, T)$, estimating $\hat{\tau} = \mu(X, 1) - \mu(X, 0)$ (flaw: regularizers often shrink treatment effect coefficients to zero in high dimensions); 2) T-Learner (Two Models): fitting separate models $\mu_1(X)$ on treatment data and $\mu_0(X)$ on control data, $\hat{\tau} = \mu_1 - \mu_0$ (flaw: fails under severe sample imbalance due to non-shared representations); 3) X-Learner: crossing imputed counterfactual residuals weighted by propensity score $e(X)$, delivering state-of-the-art robustness under severe treatment-control sample imbalance (e.g. 1% treatment rates); 4) R-Learner: optimizing Robinson's orthogonalized residual loss.

Industrial uplift production pipelines, extreme sample imbalance marketing, and benchmarking CATE estimators.

Eliminates regularization shrinkage bias in S-Learner and sample inefficiency in T-Learner under heavily skewed real-world promotional datasets.

Write the complete 4-step X-Learner algorithm detailing counterfactual residual imputation and propensity-weighted aggregation?

Why does X-Learner vastly outperform T-Learner under severe treatment-control sample imbalance (e.g. 1:100 ratio)?

Explain why GBDT greedy split selections and L1 regularization induce severe shrinkage bias on treatment effect predictions in S-Learner?

Derive R-Learner's objective via Robinson's transformation showing how residualizing outcomes and treatments yields Neyman Orthogonality?

How to deploy production-grade X-Learner and R-Learner pipelines using Microsoft EconML and Uber CausalML packages?