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Simulation-Based Inference with Waldo Confidence Regions by Leveraging Prediction Algorithms or Posterior Estimators for Inverse Problems

L Masserano, T Dorigo, R Izbicki, M Kuusela… - arXiv preprint arXiv …, 2022 - arxiv.org
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… However, an open problem in simulation-based inference (SBI) is how to construct properly calibrated confidence regions for internal parameters with nominal conditional …

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@article{2205.15680v4,
Author        = {Luca Masserano and Tommaso Dorigo and Rafael Izbicki and Mikael Kuusela and Ann B. Lee},
Title         = {Simulator-Based Inference with Waldo: Confidence Regions by Leveraging
  Prediction Algorithms and Posterior Estimators for Inverse Problems},
Eprint        = {2205.15680v4},
ArchivePrefix = {arXiv},
PrimaryClass  = {stat.ML},
Abstract      = {Prediction algorithms, such as deep neural networks (DNNs), are used in many
domain sciences to directly estimate internal parameters of interest in
simulator-based models, especially in settings where the observations include
images or complex high-dimensional data. In parallel, modern neural density
estimators, such as normalizing flows, are becoming increasingly popular for
uncertainty quantification, especially when both parameters and observations
are high-dimensional. However, parameter inference is an inverse problem and
not a prediction task; thus, an open challenge is to construct conditionally
valid and precise confidence regions, with a guaranteed probability of covering
the 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 biased
or overly confident parameter regions, yielding misleading uncertainty
estimates. This paper presents WALDO, a novel method to construct confidence
regions with finite-sample conditional validity by leveraging prediction
algorithms or posterior estimators that are currently widely adopted in SBI.
WALDO reframes the well-known Wald test statistic, and uses a computationally
efficient regression-based machinery for classical Neyman inversion of
hypothesis tests. We apply our method to a recent high-energy physics problem,
where prediction with DNNs has previously led to estimates with prediction
bias. We also illustrate how our approach can correct overly confident
posterior regions computed with normalizing flows.},
Year          = {2022},
Month         = {May},
Url           = {http://arxiv.org/abs/2205.15680v4},
File          = {2205.15680v4.pdf}
}

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