[论文解读] Generalized Bayes for Causal Inference

Emil Javurek, Dennis Frauen+2 more|arXiv (Cornell University)|Mar 3, 2026

Bayesian Modeling and Causal Inference被引用 0

一句话总结

本论文提出一种广义贝叶斯框架，在因果估计量上放置先验并用识别驱动的损失进行更新，从而在不显式似然的情况下实现不确定性量化。

ABSTRACT

Uncertainty quantification is central to many applications of causal machine learning, yet principled Bayesian inference for causal effects remains challenging. Standard Bayesian approaches typically require specifying a probabilistic model for the data-generating process, including high-dimensional nuisance components such as propensity scores and outcome regressions. Standard posteriors are thus vulnerable to strong modeling choices, including complex prior elicitation. In this paper, we propose a generalized Bayesian framework for causal inference. Our framework avoids explicit likelihood modeling; instead, we place priors directly on the causal estimands and update these using an identification-driven loss function, which yields generalized posteriors for causal effects. As a result, our framework turns existing loss-based causal estimators into estimators with full uncertainty quantification. Our framework is flexible and applicable to a broad range of causal estimands (e.g., ATE, CATE). Further, our framework can be applied on top of state-of-the-art causal machine learning pipelines (e.g., Neyman-orthogonal meta-learners). For Neyman-orthogonal losses, we show that the generalized posteriors converge to their oracle counterparts and remain robust to first-stage nuisance estimation error. With calibration, we thus obtain valid frequentist uncertainty even when nuisance estimators converge at slower-than-parametric rates. Empirically, we demonstrate that our proposed framework offers causal effect estimation with calibrated uncertainty across several causal inference settings. To the best of our knowledge, this is the first flexible framework for constructing generalized Bayesian posteriors for causal machine learning.

研究动机与目标

• Motivate uncertainty quantification in causal machine learning and address fragility of likelihood-based Bayesian methods.
• Propose a generalized Bayesian framework that uses priors on causal estimands and loss-based updating.
• Show theoretical guarantees for Neyman-orthogonal losses including robustness to nuisance estimation.
• Demonstrate empirical calibrated uncertainty across ATE, CATE, and modern causal ML pipelines.

提出的方法

• Define Gibbs/posterior q_n^S(θ|D_n) ∝ exp{−ω n L_n^S(θ; η^S)} π(θ) using an identification-driven loss L_n^S.
• Handle nuisance estimation by introducing oracle and feasible posteriors with η^S_0 and ŷ^S respectively.
• Use cross-fitting to estimate nuisances and form a cross-fitted empirical loss L_n^S(θ; ŷ^S).
• Calibrate the posterior via bootstrap-based procedures to achieve frequentist coverage.
• Prove posterior stability: for Neyman-orthogonal losses, the feasible posterior converges to the oracle at rate O_P(sqrt(n) r_n^2) where r_n is the nuisance estimation error.
• Provide algorithm (Algorithm 1) that computes feasible generalized posteriors on top of existing causal ML estimators.

Figure 1 : Overview of the pipeline for generalized Bayesian inference: In the standard causal ML pipeline, one observes the data $\mathcal{D}_{n}$ , chooses an identification-driven loss, estimates the corresponding nuisances, and thus constructs a fitting objective. Here, we further elicit a prior

实验结果

研究问题

• RQ1 Can a loss-based generalized Bayesian framework yield valid uncertainty quantification for causal estimands without explicit likelihood models?
• RQ2 Do Neyman-orthogonal losses confer posterior robustness to nuisance estimation error and enable Bernstein–von Mises-type guarantees?
• RQ3 How can one calibrate generalized posteriors to achieve frequentist coverage in practical causal ML pipelines?
• RQ4 How does the framework perform for common estimands like ATE and CATE under modern orthogonal meta-learners?

主要发现

Strategy	Orthogonal	D1	D2	D3	D4	D5	D6	D7	D8	D9
RA	✗	0.580 (0.432-0.718)	0.520 (0.374-0.663)	0.480 (0.337-0.626)	0.680 (0.533-0.805)	0.580 (0.432-0.718)	0.080 (0.022-0.192)	0.300 (0.179-0.446)	0.460 (0.318-0.607)	0.420 (0.282-0.568)
IPW	✗	1.000 (0.929-1.000)	1.000 (0.929-1.000)	1.000 (0.929-1.000)	1.000 (0.929-1.000)	1.000 (0.929-1.000)	0.420 (0.282-0.568)	0.980 (0.894-0.999)	1.000 (0.929-1.000)	1.000 (0.929-1.000)
AIPW	✓	0.940 (0.835-0.987)	0.980 (0.894-0.999)	0.980 (0.894-0.999)	0.920 (0.808-0.978)	0.940 (0.835-0.987)	0.580 (0.432-0.718)	0.940 (0.835-0.987)	0.980 (0.894-0.999)	0.940 (0.835-0.987)

• Generalized posteriors for causal effects are feasible without likelihoods and can be calibrated for frequentist coverage.
• For Neyman-orthogonal losses, the feasible posterior is asymptotically close to the oracle posterior, even if nuisances converge slowly.
• Theoretical result: posterior convergence rate in total variation is O_P(√n r_n^2) under cross-fitting, with r_n = ||η^S − η_0^S|| → 0.
• Calibration via bootstrap aligns posterior credible sets with nominal frequentist coverage.
• Empirical results show calibrated uncertainty across several causal inference settings and with state-of-the-art learners like DR-learner.

Figure 2 : CrI length for back-door ATE. Box plots of the lengths of the $95\%$ $\mathrm{CrI}^{(r)}_{0.95}$ credible interval across $R=50$ repetitions for each strategy $S\in\{\mathrm{AIPW,IPW,RA}\}$ , the dataset $\mathcal{D}_{1}$ , and a varying sample size $n\in\{100,\ldots,1000\}$ . Unfaithful