# An Easy to Interpret Diagnostic for Approximate Inference: Symmetric Divergence Over Simulations

arXiv: https://arxiv.org/abs/2103.01030 · HTML: https://mlsanity.com/paper/2103.01030/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 25 references that are in the map.
- First posted on arXiv 25 Feb 2021.

## Builds on (most cited first, 13 of 13)

- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Automatic Differentiation Variational Inference](https://mlsanity.com/paper/1603.00788/) (2016)
- [Measuring Sample Quality with Kernels](https://mlsanity.com/paper/1703.01717/) (2017)
- [R'enyi Divergence Variational Inference](https://mlsanity.com/paper/1602.02311/) (2016)
- [Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference](https://mlsanity.com/paper/1703.09194/) (2017)
- [Variational Sequential Monte Carlo](https://mlsanity.com/paper/1705.11140/) (2017)
- [Measuring Sample Quality with Stein's Method](https://mlsanity.com/paper/1506.03039/) (2015)
- [Filtering Variational Objectives](https://mlsanity.com/paper/1705.09279/) (2017)
- [Auto-Encoding Sequential Monte Carlo](https://mlsanity.com/paper/1705.10306/) (2017)
- [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)
- [Reinterpreting Importance-Weighted Autoencoders](https://mlsanity.com/paper/1704.02916/) (2017)
- [Sandwiching the marginal likelihood using bidirectional Monte Carlo](https://mlsanity.com/paper/1511.02543/) (2015)

## Built on by (most cited first, 3 of 3)

- [Probabilistic Programming with Programmable Variational Inference](https://mlsanity.com/paper/2406.15742/) (2024)
- [Discovering Inductive Bias with Gibbs Priors: A Diagnostic Tool for Approximate Bayesian Inference](https://mlsanity.com/paper/2203.03353/) (2022)
- [Discriminative calibration: Check Bayesian computation from simulations and flexible classifier](https://mlsanity.com/paper/2305.14593/) (2023)

## Abstract (arXiv)

It is important to estimate the errors of probabilistic inference algorithms. Existing diagnostics for Markov chain Monte Carlo methods assume inference is asymptotically exact, and are not appropriate for approximate methods like variational inference or Laplace's method. This paper introduces a diagnostic based on repeatedly simulating datasets from the prior and performing inference on each. The central observation is that it is possible to estimate a symmetric KL-divergence defined over these simulations.