# Variational Inference with Hamiltonian Monte Carlo

arXiv: https://arxiv.org/abs/1609.08203 · HTML: https://mlsanity.com/paper/1609.08203/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Sep 2016.

## Built on by (most cited first, 17 of 17)

- [A Survey on Uncertainty Quantification Methods for Deep Learning](https://mlsanity.com/paper/2302.13425/) (2023)
- [MCMC Variational Inference via Uncorrected Hamiltonian Annealing](https://mlsanity.com/paper/2107.04150/) (2021)
- [Langevin Diffusion Variational Inference](https://mlsanity.com/paper/2208.07743/) (2022)
- [Nested Variational Inference](https://mlsanity.com/paper/2106.11302/) (2021)
- [Surrogate Likelihoods for Variational Annealed Importance Sampling](https://mlsanity.com/paper/2112.12194/) (2021)
- [Bayesian inference via sparse Hamiltonian flows](https://mlsanity.com/paper/2203.05723/) (2022)
- [MixFlows: principled variational inference via mixed flows](https://mlsanity.com/paper/2205.07475/) (2022)
- [Alleviating Adversarial Attacks on Variational Autoencoders with MCMC](https://mlsanity.com/paper/2203.09940/) (2022)
- [Variational Inference with Locally Enhanced Bounds for Hierarchical Models](https://mlsanity.com/paper/2203.04432/) (2022)
- [Interpolating between sampling and variational inference with infinite stochastic mixtures](https://mlsanity.com/paper/2110.09618/) (2021)
- [Improving Actor-Critic Reinforcement Learning via Hamiltonian Monte Carlo Method](https://mlsanity.com/paper/2103.12020/) (2021)
- [Reparameterized Variational Rejection Sampling](https://mlsanity.com/paper/2309.14612/) (2023)
- [Differentiable Annealed Importance Sampling Minimizes The Symmetrized Kullback-Leibler Divergence Between Initial and Target Distribution](https://mlsanity.com/paper/2405.14840/) (2024)
- [Optimization of Annealed Importance Sampling Hyperparameters](https://mlsanity.com/paper/2209.13226/) (2022)
- [Asymptotically exact variational flows via involutive MCMC kernels](https://mlsanity.com/paper/2506.02162/) (2025)
- [Accelerating Hamiltonian Monte Carlo for Bayesian Inference in Neural Networks and Neural Operators](https://mlsanity.com/paper/2507.14652/) (2025)
- [Learning variational autoencoders via MCMC speed measures](https://mlsanity.com/paper/2308.13731/) (2023)

## Abstract (arXiv)

Variational inference lies at the core of many state-of-the-art algorithms. To improve the approximation of the posterior beyond parametric families, it was proposed to include MCMC steps into the variational lower bound. In this work we explore this idea using steps of the Hamiltonian Monte Carlo (HMC) algorithm, an efficient MCMC method. In particular, we incorporate the acceptance step of the HMC algorithm, guaranteeing asymptotic convergence to the true posterior. Additionally, we introduce some extensions to the HMC algorithm geared towards faster convergence. The theoretical advantages of these modifications are reflected by performance improvements in our experimental results.