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Bayesian X-Learner: Calibrated Posterior Inference for Heterogeneous Treatment Effects under Heavy-Tailed Outcomes

arXiv 2604.27394 ↗First posted 30 Apr 2026stat.ML cs.LGcited by 0

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Abstract (arXiv)

Conditional Average Treatment Effect (CATE) estimation in practice demands three properties simultaneously: heterogeneous effects τ(x), calibrated uncertainty over them, and robustness to the heavy tails that contaminate real outcome data. Meta-learners (K"unzel et al., 2019) give (i); causal forests and BART give (i)-(ii) with Gaussian-tail assumptions; no widely used tool gives all three. We present Bayesian X-Learner, an X-Learner built on cross-fitted doubly robust pseudo-outcomes (Kennedy, 2020) with a full MCMC posterior over τ(x) via a Welsch redescending pseudo-likelihood. On Hill's IHDP benchmark the default configuration attains mean √varepsilonPEHE = 0.56 on 5 replications (lowest mean; differences from S-/T-/X-learners, full-config Causal BART, and a causal forest baseline are not significant at α=0.05, and rank ordering is unstable at 10 replications -- IHDP comparisons are competitive rather than dominant). On contaminated "whale" DGPs with up to 20-25% tail density, a one-flag extension (contaminationseverity) that selects a Huber-δ nuisance loss per Huber's minimax-δ relation recovers RMSE ≈ 0.13 with tight credible intervals (single-cross-fit 30-seed coverage 83% [Wilson 66%, 93%] at 20% density; modular-Bayes pooling with Bayesian-bootstrap nuisance draws restores nominal 95% coverage).

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 29 of its 56 references that are in the map. First posted on arXiv 30 Apr 2026.

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References · 29

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17 more
  1. 2021Sensitivity Analysis of Individual Treatment Effects: A Robust Conformal Inference Approachcited by 62
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  3. 2021Quantifying Ignorance in Individual-Level Causal-Effect Estimates under Hidden Confoundingcited by 50
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  17. 2026A Doubly Robust Machine Learning Approach for Disentangling Treatment Effect Heterogeneity with Functional Outcomescited by 1

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