Bayesian inference provides principled uncertainty quantification, but accurate posterior sampling with MCMC can be computationally prohibitive for modern applications. Variational inference (VI) offers a scalable alternative and often yields accurate predictive distributions, but cheap variational families such as mean-field (MF) can produce over-concentrated approximations that miss posterior dependence. We propose variational predictive resampling (VPR), a scalable posterior sampling method that exploits VI's predictive strength within a predictive-resampling framework to better approximate the Bayesian posterior. Given a prior-likelihood pair, VPR repeatedly imputes future observations from the current variational predictive, updates the variational approximation after each imputation, and records the parameter value implied by the completed sample. We establish conditions under which the law of the parameter returned by VPR is well defined and show that its finite-horizon approximation converges to this limit. In a tractable Gaussian location model, we show that VPR with MF variational predictives converges to the exact Bayesian posterior, whereas the optimal MF-VI approximation retains a non-vanishing asymptotic gap. Experiments on linear regression, logistic regression, and hierarchical linear mixed-effects models demonstrate that VPR substantially improves posterior uncertainty quantification and recovers posterior dependence missed by MF-VI, while remaining computationally competitive with, and often more efficient than, MCMC.

翻译：贝叶斯推断提供了原则性的不确定性量化方法，但基于MCMC的精确后验采样在现代应用中可能面临巨大的计算开销。变分推断（VI）提供了一种可扩展的替代方案，通常能生成准确的预测分布，但诸如平均场（MF）等简化的变分族会产生过度集中的近似，从而忽略后验依赖关系。本文提出变分预测重采样（VPR），这是一种可扩展的后验采样方法，它在预测重采样框架中利用VI的预测优势，从而更好地逼近贝叶斯后验。给定先验-似然对，VPR反复从当前变分预测分布中插补未来观测值，每次插补后更新变分近似，并记录完整样本隐含的参数值。我们建立了VPR返回参数分布的明确定义条件，并证明其有限步近似收敛于该极限。在可解析的高斯位置模型中，我们证明采用MF变分预测的VPR可收敛至精确贝叶斯后验，而最优MF-VI近似仍存在非渐近消失的偏差。在线性回归、逻辑回归和分层线性混合效应模型上的实验表明，VPR能显著改善后验不确定性量化，恢复MF-VI遗漏的后验依赖关系，同时保持与MCMC相当的计算效率，且通常更具优势。