An Equivalence between Bayesian Priors and Penalties in Variational Inference
Machine Learning
2024-02-08 v3 Statistics Theory
Machine Learning
Statistics Theory
Abstract
In machine learning, it is common to optimize the parameters of a probabilistic model, modulated by an ad hoc regularization term that penalizes some values of the parameters. Regularization terms appear naturally in Variational Inference, a tractable way to approximate Bayesian posteriors: the loss to optimize contains a Kullback--Leibler divergence term between the approximate posterior and a Bayesian prior. We fully characterize the regularizers that can arise according to this procedure, and provide a systematic way to compute the prior corresponding to a given penalty. Such a characterization can be used to discover constraints over the penalty function, so that the overall procedure remains Bayesian.
Cite
@article{arxiv.2002.00178,
title = {An Equivalence between Bayesian Priors and Penalties in Variational Inference},
author = {Pierre Wolinski and Guillaume Charpiat and Yann Ollivier},
journal= {arXiv preprint arXiv:2002.00178},
year = {2024}
}