BibTeX

@article{2305.14275v3,
Author        = {Yash Patel and Declan McNamara and Jackson Loper and Jeffrey Regier and Ambuj Tewari},
Title         = {Variational Inference with Coverage Guarantees in Simulation-Based
  Inference},
Eprint        = {2305.14275v3},
ArchivePrefix = {arXiv},
PrimaryClass  = {stat.ME},
Abstract      = {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.},
Year          = {2023},
Month         = {May},
Url           = {http://arxiv.org/abs/2305.14275v3},
File          = {2305.14275v3.pdf}
}