Diagnostics for Variational Bayes approximations

TL;DR

This paper introduces diagnostic tools for evaluating the accuracy of Variational Bayes approximations, especially their covariance structures, and offers correction methods for large errors, demonstrated on simulated and real data.

Contribution

It presents novel diagnostics for assessing and correcting Variational Bayes approximations, focusing on covariance accuracy and applicability to various posterior aspects.

Findings

Diagnostics effectively identify approximation errors.

Correction methods improve covariance estimates.

Techniques work on both simulated and real datasets.

Abstract

Variational Bayes (VB) has shown itself to be a powerful approximation method in many application areas. This paper describes some diagnostics methods which can assess how well the VB approximates the true posterior, particularly with regards to its covariance structure. The methods proposed also allow us to generate simple corrections when the approximation error is large. It looks at joint, marginal and conditional aspects of the approximate posterior and shows how to apply these techniques in both simulated and real data examples.