Amortized variational inference is an often employed framework in simulation-based inference that 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：摊销变分推断是仿真推断中常用的框架，它能够针对任意新观测值快速计算后验近似。然而，这些近似后验的质量往往缺乏理论保证。本文提出具有保形校准的摊销神经变分推断（CANVI）方法，该流程具有可扩展性、易于实现的特点，并能提供理论保证的边缘覆盖。给定一组候选摊销后验近似器，CANVI基于每个候选构建保形预测器，通过预测效率指标比较这些预测器，并返回效率最高的预测器。CANVI确保最终得到的预测器能以用户指定的概率水平构造包含真实参数的置信区域。CANVI对候选近似器的设计决策保持不可知性，仅需从前向模型中获取样本，因此可在无似然场景中使用。我们证明了CANVI所生成区域的预测效率下界，并探讨了后验近似质量与基于该近似的预测区域效率之间的关系。最后，我们在仿真推断基准测试套件及分析星系发射光谱的重要科学任务中，验证了CANVI具有精确的校准能力和优异的预测效率。