# Variational Bayes with Intractable Likelihood

arXiv: https://arxiv.org/abs/1503.08621 · HTML: https://mlsanity.com/paper/1503.08621/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Mar 2015.

## Built on by (most cited first, 12 of 12)

- [Unifying Likelihood-free Inference with Black-box Optimization and Beyond](https://mlsanity.com/paper/2110.03372/) (2021)
- [A practical tutorial on Variational Bayes](https://mlsanity.com/paper/2103.01327/) (2021)
- [Quantum Speedup of Natural Gradient for Variational Bayes](https://mlsanity.com/paper/2106.05807/) (2021)
- [Wasserstein Gaussianization and Efficient Variational Bayes for Robust Bayesian Synthetic Likelihood](https://mlsanity.com/paper/2305.14746/) (2023)
- [Variational Pseudo Marginal Methods for Jet Reconstruction in Particle Physics](https://mlsanity.com/paper/2406.03242/) (2024)
- [Efficient Discretizations of Optimal Transport](https://mlsanity.com/paper/2102.07956/) (2021)
- [Natural Gradient Hybrid Variational Inference with Application to Deep Mixed Models](https://mlsanity.com/paper/2302.13536/) (2023)
- [Leveraging Nested MLMC for Sequential Neural Posterior Estimation with Intractable Likelihoods](https://mlsanity.com/paper/2401.16776/) (2024)
- [You Only Accept Samples Once: Fast, Self-Correcting Stochastic Variational Inference](https://mlsanity.com/paper/2406.02838/) (2024)
- [A Statistical Framework for Model Selection in LSTM Networks](https://mlsanity.com/paper/2506.06840/) (2025)
- [Variational Approximated Restricted Maximum Likelihood Estimation for Spatial Data](https://mlsanity.com/paper/2604.07635/) (2026)
- [Dynestyx: A Probabilistic Programming Library for Dynamical Systems](https://mlsanity.com/paper/2606.16985/) (2026)

## Abstract (arXiv)

Variational Bayes (VB) is rapidly becoming a popular tool for Bayesian inference in statistical modeling. However, the existing VB algorithms are restricted to cases where the likelihood is tractable, which precludes the use of VB in many interesting situations such as in state space models and in approximate Bayesian computation (ABC), where application of VB methods was previously impossible. This paper extends the scope of application of VB to cases where the likelihood is intractable, but can be estimated unbiasedly. The proposed VB method therefore makes it possible to carry out Bayesian inference in many statistical applications, including state space models and ABC. The method is generic in the sense that it can be applied to almost all statistical models without requiring too much model-based derivation, which is a drawback of many existing VB algorithms. We also show how the proposed method can be used to obtain highly accurate VB approximations of marginal posterior distributions.