# Learning Approximately Objective Priors

## TL;DR

This paper introduces a method to learn approximate objective priors in Bayesian models by optimizing a parametric family to closely match intractable reference priors, demonstrated on Jeffreys and VAE priors.

## Contribution

It proposes a novel technique for approximating complex objective priors using a parametric family and black-box optimization, addressing intractability issues.

## Key findings

- Successfully recovers Jeffreys priors for various models.
- Learns reference prior for Variational Autoencoders.
- Demonstrates effectiveness through experimental results.

## Abstract

Informative Bayesian priors are often difficult to elicit, and when this is the case, modelers usually turn to noninformative or objective priors. However, objective priors such as the Jeffreys and reference priors are not tractable to derive for many models of interest. We address this issue by proposing techniques for learning reference prior approximations: we select a parametric family and optimize a black-box lower bound on the reference prior objective to find the member of the family that serves as a good approximation. We experimentally demonstrate the method's effectiveness by recovering Jeffreys priors and learning the Variational Autoencoder's reference prior.