# Stochastic Variance-Reduced Hamilton Monte Carlo Methods

arXiv: https://arxiv.org/abs/1802.04791 · HTML: https://mlsanity.com/paper/1802.04791/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2018.

## Built on by (most cited first, 7 of 7)

- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Distributed Learning Systems with First-order Methods](https://mlsanity.com/paper/2104.05245/) (2021)
- [Accelerating Approximate Thompson Sampling with Underdamped Langevin Monte Carlo](https://mlsanity.com/paper/2401.11665/) (2024)
- [Feel-Good Thompson Sampling for Contextual Bandits: a Markov Chain Monte Carlo Showdown](https://mlsanity.com/paper/2507.15290/) (2025)
- [Log-concave Sampling from a Convex Body with a Barrier: a Robust and Unified Dikin Walk](https://mlsanity.com/paper/2410.05700/) (2024)
- [Subsampling Error in Stochastic Gradient Langevin Diffusions](https://mlsanity.com/paper/2305.13882/) (2023)
- [A New Framework for Variance-Reduced Hamiltonian Monte Carlo](https://mlsanity.com/paper/2102.04613/) (2021)

## Abstract (arXiv)

We propose a fast stochastic Hamilton Monte Carlo (HMC) method, for sampling from a smooth and strongly log-concave distribution. At the core of our proposed method is a variance reduction technique inspired by the recent advance in stochastic optimization. We show that, to achieve ε accuracy in 2-Wasserstein distance, our algorithm achieves tilde O(n+kappa2d1/2/ε+kappa4/3d1/3n2/3/ε2/3) gradient complexity (i.e., number of component gradient evaluations), which outperforms the state-of-the-art HMC and stochastic gradient HMC methods in a wide regime. We also extend our algorithm for sampling from smooth and general log-concave distributions, and prove the corresponding gradient complexity as well. Experiments on both synthetic and real data demonstrate the superior performance of our algorithm.