# A Targeted Accuracy Diagnostic for Variational Approximations

## TL;DR

This paper introduces TADDAA, a diagnostic tool that uses multiple short MCMC chains to accurately assess the error in specific posterior functionals of variational approximations, improving evaluation in complex models.

## Contribution

The paper presents TADDAA, a novel targeted diagnostic method that provides lower bounds on the error of posterior functionals using short MCMC chains, addressing limitations of existing diagnostics.

## Key findings

- TADDAA effectively estimates errors in variational posterior functionals.
- The method is computationally efficient and practical for complex models.
- Numerical experiments demonstrate TADDAA's utility on real and synthetic data.

## Abstract

Variational Inference (VI) is an attractive alternative to Markov Chain Monte Carlo (MCMC) due to its computational efficiency in the case of large datasets and/or complex models with high-dimensional parameters. However, evaluating the accuracy of variational approximations remains a challenge. Existing methods characterize the quality of the whole variational distribution, which is almost always poor in realistic applications, even if specific posterior functionals such as the component-wise means or variances are accurate. Hence, these diagnostics are of practical value only in limited circumstances. To address this issue, we propose the TArgeted Diagnostic for Distribution Approximation Accuracy (TADDAA), which uses many short parallel MCMC chains to obtain lower bounds on the error of each posterior functional of interest. We also develop a reliability check for TADDAA to determine when the lower bounds should not be trusted. Numerical experiments validate the practical utility and computational efficiency of our approach on a range of synthetic distributions and real-data examples, including sparse logistic regression and Bayesian neural network models.