BibTeX

@article{2412.16419v1,
Author        = {Laura Battaglia and Geoff Nicholls},
Title         = {Amortising Variational Bayesian Inference over prior hyperparameters
  with a Normalising Flow},
Eprint        = {2412.16419v1},
ArchivePrefix = {arXiv},
PrimaryClass  = {stat.CO},
Abstract      = {In Bayesian inference prior hyperparameters are chosen subjectively or
estimated using empirical Bayes methods. Generalised Bayesian Inference also
has hyperparameters (the learning rate, and parameters of the loss). As part of
the Generalised-Bayes workflow it is necessary to check sensitivity to the
choice of hyperparameters, but running MCMC or fitting a variational
approximation at each hyperparameter setting is impractical when there are more
than a few hyperparameters. Simulation Based Inference has been used to
amortise over data and hyperparameters and can be useful for Bayesian problems.
However, there is no Simulation Based Inference for Generalised Bayes
posteriors, as there is no generative model for the data. Working with a
variational family parameterised by a normalising flow, we show how to fit a
variational Generalised Bayes posterior, amortised over all hyperparameters.
This may be sampled very efficiently at different hyperparameter values without
refitting, and supports efficient robustness checks and hyperparameter
selection. We show that there exist amortised normalising-flow architectures
which are universal approximators. We test our approach on a relatively
large-scale application of Generalised Bayesian Inference. The code is
available online.},
Year          = {2024},
Month         = {Dec},
Url           = {http://arxiv.org/abs/2412.16419v1},
File          = {2412.16419v1.pdf}
}