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Amortized variational inference produces a posterior approximation that canbe rapidly computed given any new observation. Unfortunately, there are fewguarantees about the quality of these approximate posteriors. We proposeConformalized Amortized Neural Variational Inference (CANVI), a procedure thatis scalable, easily implemented, and provides guaranteed marginal coverage.Given a collection of candidate amortized posterior approximators, CANVIconstructs conformalized predictors based on each candidate, compares thepredictors using a metric known as predictive efficiency, and returns the mostefficient predictor. CANVI ensures that the resulting predictor constructsregions that contain the truth with a user-specified level of probability.CANVI is agnostic to design decisions in formulating the candidateapproximators and only requires access to samples from the forward model,permitting its use in likelihood-free settings. We prove lower bounds on thepredictive efficiency of the regions produced by CANVI and explore how thequality of a posterior approximation relates to the predictive efficiency ofprediction regions based on that approximation. Finally, we demonstrate theaccurate calibration and high predictive efficiency of CANVI on a suite ofsimulation-based inference benchmark tasks and an important scientific task:analyzing galaxy emission spectra.

Amortized Variational Inference with Coverage Guarantees