# Langevin Markov Chain Monte Carlo with stochastic gradients

arXiv: https://arxiv.org/abs/1805.08863 · HTML: https://mlsanity.com/paper/1805.08863/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 May 2018.

## Built on by (most cited first, 2 of 2)

- [Exact Langevin Dynamics with Stochastic Gradients](https://mlsanity.com/paper/2102.01691/) (2021)
- [Quantifying the mini-batching error in Bayesian inference for Adaptive Langevin dynamics](https://mlsanity.com/paper/2105.10347/) (2021)

## Abstract (arXiv)

Monte Carlo sampling techniques have broad applications in machine learning, Bayesian posterior inference, and parameter estimation. Often the target distribution takes the form of a product distribution over a dataset with a large number of entries. For sampling schemes utilizing gradient information it is cheaper for the derivative to be approximated using a random small subset of the data, introducing extra noise into the system. We present a new discretization scheme for underdamped Langevin dynamics when utilizing a stochastic (noisy) gradient. This scheme is shown to bias computed averages to second order in the stepsize while giving exact results in the special case of sampling a Gaussian distribution with a normally distributed stochastic gradient.