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Generalized Bayes for Causal Inference

NeurIPS 2026 · Probabilistic and scientific modeling › Treatment effects · approach: Latent-variable causal inference · 0 citations (OpenAlex)

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Proposes a generalized (Gibbs) Bayes framework for causal inference that places priors directly on causal estimands and updates them with Neyman-orthogonal identification-driven losses, with cross-fitting and bootstrap calibration of the learning rate omega.

Problem

Bayesian uncertainty quantification for causal effects is fragile because likelihood-based approaches require high-dimensional nuisance models (propensity scores, outcome regressions), priors on nuisances, and suffer from regularization-induced confounding and feedback problems.

Approach

Replace the likelihood with an identification-driven loss on the causal estimand (e.g., AIPW/DR squared loss), put a prior directly on the estimand, and form a Gibbs posterior exp(-omega n L_n) pi; with Neyman-orthogonal losses and cross-fitting, the feasible posterior is stable to first-stage nuisance error (TV = O(sqrt(n) r_n^2)), and omega is calibrated by bootstrap for frequentist coverage.

Key results

• AIPW-based generalized posterior achieves the most accurate 95% credible interval coverage across all 9 synthetic ATE datasets (n=1000, R=50).
• Among faithful intervals, AIPW credible intervals are the narrowest, and CrI length shrinks as sample size grows.
• Theory: feasible posterior is within TV O(sqrt(n) r_n^2) of the oracle posterior for Neyman-orthogonal losses, so r_n=o(n^{-1/4}) suffices for BvM.

Limitations

• Empirical validation limited to synthetic back-door ATE experiments in the main text; CATE results deferred to appendix.
• Frequentist validity relies on a Bernstein-von Mises approximation and on bootstrap calibration of omega, whose assumptions are stated as conditions rather than verified in general.
• Non-orthogonal losses yield posterior instability that scales with r_n rather than r_n^2.

Experimental setup

Datasets: 9 synthetic backdoor ATE datasets

Benchmarks: 9 synthetic backdoor ATE datasets

Metrics: 95% credible interval coverage credible interval length

Baselines: RA IPW AIPW

Builds on: Gibbs posterior DR-learner double machine learning Bernstein-von Mises for generalized posteriors

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