mlsanityData to 7 Oct 2026

Revisiting the Effects of Stochasticity for Hamiltonian Samplers

arXiv 2106.16200 ↗First posted 30 Jun 2021cs.LG stat.COcited by 3

Not on the map. Why?

Abstract (arXiv)

We revisit the theoretical properties of Hamiltonian stochastic differential equations (SDES) for Bayesian posterior sampling, and we study the two types of errors that arise from numerical SDE simulation: the discretization error and the error due to noisy gradient estimates in the context of data subsampling. Our main result is a novel analysis for the effect of mini-batches through the lens of differential operator splitting, revising previous literature results. The stochastic component of a Hamiltonian SDE is decoupled from the gradient noise, for which we make no normality assumptions. This leads to the identification of a convergence bottleneck: when considering mini-batches, the best achievable error rate is O(η2), with η being the integrator step size. Our theoretical results are supported by an empirical study on a variety of regression and classification tasks for Bayesian neural networks.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 20 of its 72 references that are in the map. First posted on arXiv 30 Jun 2021.

Builds on

20 of 72 references.

References · 20

  1. 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,597
  2. 2014Stochastic Gradient Hamiltonian Monte Carlocited by 341
  3. 2017Stochastic Gradient Descent as Approximate Bayesian Inferencecited by 298
  4. 2020Finite Versus Infinite Neural Networks: an Empirical Studycited by 156
  5. 2015A Complete Recipe for Stochastic Gradient MCMCcited by 146
  6. 2017Stochastic gradient descent performs variational inference, converges to limit cycles for deep networkscited by 108
  7. 2017Global Convergence of Langevin Dynamics Based Algorithms for Nonconvex Optimizationcited by 96
  8. 2018Random Shuffling Beats SGD after Finite Epochscited by 66
  9. 2020All You Need is a Good Functional Prior for Bayesian Deep Learningcited by 61
  10. 2020Scaling Hamiltonian Monte Carlo Inference for Bayesian Neural Networks with Symmetric Splittingcited by 54
  11. 2018Fluctuation-dissipation relations for stochastic gradient descentcited by 47
  12. 2016On the Convergence of Stochastic Gradient MCMC Algorithms with High-Order Integratorscited by 35
8 more
  1. 2020On Learning Rates and Schr"odinger Operatorscited by 33
  2. 2018Global Convergence of Stochastic Gradient Hamiltonian Monte Carlo for Non-Convex Stochastic Optimization: Non-Asymptotic Performance Bounds and Momentum-Based Accelerationcited by 31
  3. 2019Conformal Symplectic and Relativistic Optimizationcited by 28
  4. 2020On dissipative symplectic integration with applications to gradient-based optimizationcited by 23
  5. 2018On the Importance of Strong Baselines in Bayesian Deep Learningcited by 12
  6. 2018Breaking Reversibility Accelerates Langevin Dynamics for Global Non-Convex Optimizationcited by 12
  7. 2015Covariance-Controlled Adaptive Langevin Thermostat for Large-Scale Bayesian Samplingcited by 10
  8. 2016Pseudo-Marginal Hamiltonian Monte Carlocited by 6

Built on by

Cited by year

Citing papers per year: 2023: 1; 2024: 1; 2025: 1.

3 papers.

  1. 2024Sampling from Bayesian Neural Network Posteriors with Symmetric Minibatch Splitting Langevin Dynamicscited by 12
  2. 2023On permutation symmetries in Bayesian neural network posteriors: a variational perspectivecited by 4
  3. 2025Randomised Splitting Methods and Stochastic Gradient Descentcited by 3