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Preferential Subsampling for Stochastic Gradient Langevin Dynamics

arXiv 2210.16189 ↗First posted 28 Oct 2022stat.ML cs.LG stat.COcited by 0

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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.

Key facts. No citing papers in the map yet (data through 13 Oct 2026). Builds on 21 of its 37 references that are in the map. First posted on arXiv 28 Oct 2022.

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21 of 37 references.

References · 21

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,093
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  12. 2019Stochastic gradient Markov chain Monte Carlocited by 56
9 more
  1. 2017Control Variates for Stochastic Gradient MCMCcited by 25
  2. 2014Accelerating Minibatch Stochastic Gradient Descent using Stratified Samplingcited by 21
  3. 2018On the Theory of Variance Reduction for Stochastic Gradient Monte Carlocited by 19
  4. 2020Adam with Bandit Sampling for Deep Learningcited by 10
  5. 2017Determinantal Point Processes for Mini-Batch Diversificationcited by 8
  6. 2017Stochastic Optimization with Bandit Samplingcited by 8
  7. 2015Non-Uniform Stochastic Average Gradient Method for Training Conditional Random Fieldscited by 6
  8. 2017A Convergence Analysis for A Class of Practical Variance-Reduction Stochastic Gradient MCMCcited by 3
  9. 2020Improving Sampling Accuracy of Stochastic Gradient MCMC Methods via Non-uniform Subsampling of Gradientscited by 2

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