# An Equivalence between Bayesian Priors and Penalties in Variational Inference

arXiv: https://arxiv.org/abs/2002.00178 · HTML: https://mlsanity.com/paper/2002.00178/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Feb 2020.

## Built on by (most cited first, 1 of 1)

- [Deep neural networks with dependent weights: Gaussian Process mixture limit, heavy tails, sparsity and compressibility](https://mlsanity.com/paper/2205.08187/) (2022)

## Abstract (arXiv)

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.