Amortized variational inference produces a posterior approximation that can be rapidly computed 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 a user-specified level of probability. 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：摊销变分推断能够针对任意新观测数据快速生成后验近似，但此类近似后验的质量鲜有理论保障。本文提出保形摊销神经变分推断（CANVI）方法，该算法具有可扩展性、易于实现，并提供有保证的边际覆盖。对于一组候选摊销后验近似器，CANVI基于每个候选构造保形预测器，通过称为预测效率的指标比较各预测器，并返回效率最高的预测器。CANVI确保其生成的预测区域以用户指定的概率包含真实值。该方法对候选近似器的设计决策具有不可知性，仅需访问前向模型的样本，因此适用于无似然场景。我们证明了CANVI生成区域预测效率的下界，并探究后验近似质量与基于该近似构建的预测区域效率之间的关系。最后，在一系列基于模拟的推理基准任务及重要科学任务（星系发射光谱分析）中，验证了CANVI的精确校准能力与高预测效率。