让后验分布更贴近真实数据生成过程，提升预测准确性。
Predictive variational inference: Learn the predictively optimal posterior distribution
- 直接优化预测效果而非逼近贝叶斯后验
- 在真实数据上显著改善预测性能
- 可自动发现参数异质性，适合模型诊断
经典变分推断旨在逼近贝叶斯后验，但在模型误设下，即使精确的后验也无意义。本文提出预测变分推断（PVI）：一种通用推断框架，通过多个评分规则衡量预测分布与真实数据生成过程的接近程度，直接寻找最优后验密度并从中采样。该方法不追求逼近贝叶斯后验，甚至在渐近情况下也不相同，而是被视为隐式的层级扩展。学习到的后验不确定性可识别群体中参数的异质性，实现自动模型诊断。该框架适用于似然精确与似然无模型场景，并在真实数据中得到验证。
原文摘要 · Abstract (English)
Vanilla variational inference finds an optimal approximation to the Bayesian posterior distribution, but even the exact Bayesian posterior is often not meaningful under model misspecification. We propose predictive variational inference (PVI): a general inference framework that seeks and samples from an optimal posterior density such that the resulting posterior predictive distribution is as close to the true data generating process as possible, while this closeness is measured by multiple scoring rules. By optimizing the objective, the predictive variational inference is generally not the same as, or even attempting to approximate, the Bayesian posterior, even asymptotically. Rather, we interpret it as implicit hierarchical expansion. Further, the learned posterior uncertainty detects heterogeneity of parameters among the population, enabling automatic model diagnosis. This framework applies to both likelihood-exact and likelihood-free models. We demonstrate its application in real data examples.
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