# A Targeted Accuracy Diagnostic for Variational Approximations

arXiv: https://arxiv.org/abs/2302.12419 · HTML: https://mlsanity.com/paper/2302.12419/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 58 references that are in the map.
- First posted on arXiv 24 Feb 2023.

## Builds on (most cited first, 19 of 19)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [Automatic Differentiation Variational Inference](https://mlsanity.com/paper/1603.00788/) (2016)
- [Measuring Sample Quality with Kernels](https://mlsanity.com/paper/1703.01717/) (2017)
- [Measuring Sample Quality with Stein's Method](https://mlsanity.com/paper/1506.03039/) (2015)
- [Rank-normalization, folding, and localization: An improved widehatR for assessing convergence of MCMC](https://mlsanity.com/paper/1903.08008/) (2019)
- [Importance Weighting and Variational Inference](https://mlsanity.com/paper/1808.09034/) (2018)
- [Yes, but Did It Work?: Evaluating Variational Inference](https://mlsanity.com/paper/1802.02538/) (2018)
- [Sparsity information and regularization in the horseshoe and other shrinkage priors](https://mlsanity.com/paper/1707.01694/) (2017)
- [Advances in Black-Box VI: Normalizing Flows, Importance Weighting, and Optimization](https://mlsanity.com/paper/2006.10343/) (2020)
- [Validated Variational Inference via Practical Posterior Error Bounds](https://mlsanity.com/paper/1910.04102/) (2019)
- [The Barker proposal: combining robustness and efficiency in gradient-based MCMC](https://mlsanity.com/paper/1908.11812/) (2019)
- [Revisiting the Gelman-Rubin Diagnostic](https://mlsanity.com/paper/1812.09384/) (2018)
- [A Framework for Improving the Reliability of Black-box Variational Inference](https://mlsanity.com/paper/2203.15945/) (2022)
- [Statistical and Computational Trade-offs in Variational Inference: A Case Study in Inferential Model Selection](https://mlsanity.com/paper/2207.11208/) (2022)
- [Convergence of position-dependent MALA with application to conditional simulation in GLMMs](https://mlsanity.com/paper/2108.12662/) (2021)

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

- [Amortized Bayesian Workflow](https://mlsanity.com/paper/2409.04332/) (2024)

## Abstract (arXiv)

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.