Amortized variational inference produces a posterior approximator that can compute a posterior approximation given any new observation. Unfortunately, there are few guarantees about the quality of these approximate posteriors. We propose Conformalized Amortized Neural Variational Inference (CANVI), a procedure that is scalable, easily implemented, and provides guaranteed marginal coverage. Given a collection of candidate amortized posterior approximators, CANVI constructs conformalized predictors based on each candidate, compares the predictors using a metric known as predictive efficiency, and returns the most efficient predictor. CANVI ensures that the resulting predictor constructs regions that contain the truth with high probability (exactly how high is prespecified by the user). CANVI is agnostic to design decisions in formulating the candidate approximators and only requires access to samples from the forward model, permitting its use in likelihood-free settings. We prove lower bounds on the predictive efficiency of the regions produced by CANVI and explore how the quality of a posterior approximation relates to the predictive efficiency of prediction regions based on that approximation. Finally, we demonstrate the accurate calibration and high predictive efficiency of CANVI on a suite of simulation-based inference benchmark tasks and an important scientific task: analyzing galaxy emission spectra.

翻译：摊销变分推断能够生成一个后验逼近器，该逼近器可在给定任何新观测数据时计算后验近似。然而，这些近似后验的质量缺乏保证。我们提出一种可扩展、易于实现且提供保证边际覆盖的流程——共形化摊销神经变分推断（CANVI）。给定一组候选摊销后验逼近器，CANVI基于每个候选构建共形化预测器，通过称为预测效率的度量比较各预测器，并返回最高效的预测器。CANVI确保最终预测器所构建的区域以高概率（具体概率由用户预设）包含真实值。CANVI对候选逼近器的设计决策保持无关性，仅需访问前向模型的样本，从而适用于无似然场景。我们证明了CANVI所生成区域的预测效率下界，并探究后验逼近质量如何影响基于该逼近的预测区域的预测效率。最后，在一系列基于模拟的推断基准任务以及一项重要科学任务——分析星系发射光谱中，我们验证了CANVI的准确校准性与高预测效率。