提出贝叶斯X-learner，实现重尾结果下的处理效应估计与可信区间校准。
Bayesian X-Learner: Calibrated Posterior Inference for Heterogeneous Treatment Effects under Heavy-Tailed Outcomes
- 基于交叉拟合双重稳健伪结果，构建全后验推断的贝叶斯框架。
- 在重尾数据下仍保持低均方误差（约0.13）和紧致可信区间。
- 适合需高可靠性不确定性量化的真实世界因果推断场景。
实际中条件平均处理效应（CATE）估计需要同时满足三个特性：异质性效应τ(x)、对其的校准不确定性以及对真实数据中重尾干扰的鲁棒性。现有方法如元学习器（Meta-learners）提供异质性；因果森林与BART在高斯尾假设下可实现前两点；但尚无广泛使用的工具能兼顾三者。本文提出贝叶斯X-learner，基于交叉拟合双重稳健伪结果（Kennedy, 2020），通过威爾許红降似然函数实现τ(x)的完整马尔可夫链蒙特卡洛后验推断。在Hill的IHDP基准上，默认配置在5次重复中达到均方根PEHE = 0.56（最低均值；与S-/T-/X-learner、全配置因果BART及因果森林基线差异不显著，α=0.05水平下排名不稳定）。在含最多20%-25%尾部密度的‘鲸鱼’生成模型下，引入单标志扩展（contamination_severity）自动选择基于霍伯最小最大δ关系的Huber-δ损失，恢复均方误差≈0.13，并获得紧密可信区间（单交叉拟合30种子覆盖率为83% [威尔逊区间66%, 93%]，在20%尾部密度下）；模块化贝叶斯池化结合贝叶斯自助抽样恢复名义95%覆盖率。
原文摘要 · Abstract (English)
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 (Künzel 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 $\sqrt{\varepsilon_{\mathrm{PEHE}}} = 0.56$ 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 (contamination_severity) that selects a Huber-$δ$ nuisance loss per Huber's minimax-$δ$ relation recovers RMSE $\approx 0.13$ 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).
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