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Prediction algorithms, such as deep neural networks (DNNs), are used in manydomain sciences to directly estimate internal parameters of interest insimulator-based models, especially in settings where the observations includeimages or complex high-dimensional data. In parallel, modern neural densityestimators, such as normalizing flows, are becoming increasingly popular foruncertainty quantification, especially when both parameters and observationsare high-dimensional. However, parameter inference is an inverse problem andnot a prediction task; thus, an open challenge is to construct conditionallyvalid and precise confidence regions, with a guaranteed probability of coveringthe true parameters of the data-generating process, no matter what the(unknown) parameter values are, and without relying on large-sample theory.Many simulator-based inference (SBI) methods are indeed known to produce biasedor overly confident parameter regions, yielding misleading uncertaintyestimates. This paper presents WALDO, a novel method to construct confidenceregions with finite-sample conditional validity by leveraging predictionalgorithms or posterior estimators that are currently widely adopted in SBI.WALDO reframes the well-known Wald test statistic, and uses a computationallyefficient regression-based machinery for classical Neyman inversion ofhypothesis tests. We apply our method to a recent high-energy physics problem,where prediction with DNNs has previously led to estimates with predictionbias. We also illustrate how our approach can correct overly confidentposterior regions computed with normalizing flows.

Simulator-Based Inference with Waldo: Confidence Regions by Leveraging Prediction Algorithms and Posterior Estimators for Inverse Problems