# Preferential Subsampling for Stochastic Gradient Langevin Dynamics

arXiv: https://arxiv.org/abs/2210.16189 · HTML: https://mlsanity.com/paper/2210.16189/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 37 references that are in the map.
- First posted on arXiv 28 Oct 2022.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [Minimizing Finite Sums with the Stochastic Average Gradient](https://mlsanity.com/paper/1309.2388/) (2013)
- [High-dimensional Bayesian inference via the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1605.01559/) (2016)
- [Measuring Sample Quality with Kernels](https://mlsanity.com/paper/1703.01717/) (2017)
- [Log-concave sampling: Metropolis-Hastings algorithms are fast](https://mlsanity.com/paper/1801.02309/) (2018)
- [User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient](https://mlsanity.com/paper/1710.00095/) (2017)
- [Stochastic Optimization with Importance Sampling](https://mlsanity.com/paper/1401.2753/) (2014)
- [Consistency and fluctuations for stochastic gradient Langevin dynamics](https://mlsanity.com/paper/1409.0578/) (2014)
- [Stochastic gradient Markov chain Monte Carlo](https://mlsanity.com/paper/1907.06986/) (2019)
- [Control Variates for Stochastic Gradient MCMC](https://mlsanity.com/paper/1706.05439/) (2017)
- [Accelerating Minibatch Stochastic Gradient Descent using Stratified Sampling](https://mlsanity.com/paper/1405.3080/) (2014)
- [On the Theory of Variance Reduction for Stochastic Gradient Monte Carlo](https://mlsanity.com/paper/1802.05431/) (2018)
- [Adam with Bandit Sampling for Deep Learning](https://mlsanity.com/paper/2010.12986/) (2020)
- [Stochastic Optimization with Bandit Sampling](https://mlsanity.com/paper/1708.02544/) (2017)
- [Determinantal Point Processes for Mini-Batch Diversification](https://mlsanity.com/paper/1705.00607/) (2017)
- [Non-Uniform Stochastic Average Gradient Method for Training Conditional Random Fields](https://mlsanity.com/paper/1504.04406/) (2015)
- [A Convergence Analysis for A Class of Practical Variance-Reduction Stochastic Gradient MCMC](https://mlsanity.com/paper/1709.01180/) (2017)
- [Improving Sampling Accuracy of Stochastic Gradient MCMC Methods via Non-uniform Subsampling of Gradients](https://mlsanity.com/paper/2002.08949/) (2020)

## Abstract (arXiv)

Stochastic gradient MCMC (SGMCMC) offers a scalable alternative to traditional MCMC, by constructing an unbiased estimate of the gradient of the log-posterior with a small, uniformly-weighted subsample of the data. While efficient to compute, the resulting gradient estimator may exhibit a high variance and impact sampler performance. The problem of variance control has been traditionally addressed by constructing a better stochastic gradient estimator, often using control variates. We propose to use a discrete, non-uniform probability distribution to preferentially subsample data points that have a greater impact on the stochastic gradient. In addition, we present a method of adaptively adjusting the subsample size at each iteration of the algorithm, so that we increase the subsample size in areas of the sample space where the gradient is harder to estimate. We demonstrate that such an approach can maintain the same level of accuracy while substantially reducing the average subsample size that is used.