# Variational Hamiltonian Monte Carlo via Score Matching

arXiv: https://arxiv.org/abs/1602.02219 · HTML: https://mlsanity.com/paper/1602.02219/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Feb 2016.

## Built on by (most cited first, 14 of 14)

- [Uncertainty Quantification in Machine Learning for Engineering Design and Health Prognostics: A Tutorial](https://mlsanity.com/paper/2305.04933/) (2023)
- [Batch and match: black-box variational inference with a score-based divergence](https://mlsanity.com/paper/2402.14758/) (2024)
- [Semi-Implicit Variational Inference via Score Matching](https://mlsanity.com/paper/2308.10014/) (2023)
- [Proper scoring rules for estimation and forecast evaluation](https://mlsanity.com/paper/2504.01781/) (2025)
- [Hierarchical Semi-Implicit Variational Inference with Application to Diffusion Model Acceleration](https://mlsanity.com/paper/2310.17153/) (2023)
- [EigenVI: score-based variational inference with orthogonal function expansions](https://mlsanity.com/paper/2410.24054/) (2024)
- [Kernel Semi-Implicit Variational Inference](https://mlsanity.com/paper/2405.18997/) (2024)
- [Batch, match, and patch: low-rank approximations for score-based variational inference](https://mlsanity.com/paper/2410.22292/) (2024)
- [Dimension reduction via score ratio matching](https://mlsanity.com/paper/2410.19990/) (2024)
- [Uncertainty Quantification of Graph Convolution Neural Network Models of Evolving Processes](https://mlsanity.com/paper/2402.11179/) (2024)
- [Semi-Implicit Functional Gradient Flow for Efficient Sampling](https://mlsanity.com/paper/2410.17935/) (2024)
- [A Kernel Approach for Semi-implicit Variational Inference](https://mlsanity.com/paper/2601.12023/) (2026)
- [Large-scale Score-based Variational Posterior Inference for Bayesian Deep Neural Networks](https://mlsanity.com/paper/2602.05873/) (2026)
- [Neural-Inspired Posterior Approximation (NIPA)](https://mlsanity.com/paper/2601.22539/) (2026)

## Abstract (arXiv)

Traditionally, the field of computational Bayesian statistics has been divided into two main subfields: variational methods and Markov chain Monte Carlo (MCMC). In recent years, however, several methods have been proposed based on combining variational Bayesian inference and MCMC simulation in order to improve their overall accuracy and computational efficiency. This marriage of fast evaluation and flexible approximation provides a promising means of designing scalable Bayesian inference methods. In this paper, we explore the possibility of incorporating variational approximation into a state-of-the-art MCMC method, Hamiltonian Monte Carlo (HMC), to reduce the required gradient computation in the simulation of Hamiltonian flow, which is the bottleneck for many applications of HMC in big data problems. To this end, we use a it free-form approximation induced by a fast and flexible surrogate function based on single-hidden layer feedforward neural networks. The surrogate provides sufficiently accurate approximation while allowing for fast exploration of parameter space, resulting in an efficient approximate inference algorithm. We demonstrate the advantages of our method on both synthetic and real data problems.