# Wasserstein Gaussianization and Efficient Variational Bayes for Robust Bayesian Synthetic Likelihood

arXiv: https://arxiv.org/abs/2305.14746 · HTML: https://mlsanity.com/paper/2305.14746/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 44 references that are in the map.
- First posted on arXiv 24 May 2023.

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

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problem](https://mlsanity.com/paper/1802.08089/) (2018)
- [Bayesian Synthetic Likelihood](https://mlsanity.com/paper/2305.05120/) (2023)
- [First-order Conditions for Optimization in the Wasserstein Space](https://mlsanity.com/paper/2209.12197/) (2022)
- [Robust Approximate Bayesian Inference with Synthetic Likelihood](https://mlsanity.com/paper/1904.04551/) (2019)
- [Variational Bayes with Intractable Likelihood](https://mlsanity.com/paper/1503.08621/) (2015)
- [Bayesian Indirect Inference Using a Parametric Auxiliary Model](https://mlsanity.com/paper/1505.03372/) (2015)
- [Fast and Accurate Variational Inference for Models with Many Latent Variables](https://mlsanity.com/paper/2005.07430/) (2020)
- [Variational Bayes with Synthetic Likelihood](https://mlsanity.com/paper/1608.03069/) (2016)
- [Robust Bayesian Synthetic Likelihood via a Semi-Parametric Approach](https://mlsanity.com/paper/1809.05800/) (2018)
- [Efficient Bayesian synthetic likelihood with whitening transformations](https://mlsanity.com/paper/1909.04857/) (2019)
- [The block-Poisson estimator for optimally tuned exact subsampling MCMC](https://mlsanity.com/paper/1603.08232/) (2016)

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

- [Simulation-based Bayesian inference under model misspecification](https://mlsanity.com/paper/2503.12315/) (2025)

## Abstract (arXiv)

The Bayesian Synthetic Likelihood (BSL) method is a widely-used tool for likelihood-free Bayesian inference. This method assumes that some summary statistics are normally distributed, which can be incorrect in many applications. We propose a transformation, called the Wasserstein Gaussianization transformation, that uses a Wasserstein gradient flow to approximately transform the distribution of the summary statistics into a Gaussian distribution. BSL also implicitly requires compatibility between simulated summary statistics under the working model and the observed summary statistics. A robust BSL variant which achieves this has been developed in the recent literature. We combine the Wasserstein Gaussianization transformation with robust BSL, and an efficient Variational Bayes procedure for posterior approximation, to develop a highly efficient and reliable approximate Bayesian inference method for likelihood-free problems.