mlsanityData to 14 Oct 2026

On Convergence of the Alternating Directions SGHMC Algorithm

arXiv 2405.13140 ↗First posted 21 May 2024math.ST cs.LG math.PRcited by 0

Not on the map. Why?

Abstract (arXiv)

We study convergence rates of Hamiltonian Monte Carlo (HMC) algorithms with leapfrog integration under mild conditions on stochastic gradient oracle for the target distribution (SGHMC). Our method extends standard HMC by allowing the use of general auxiliary distributions, which is achieved by a novel procedure of Alternating Directions. The convergence analysis is based on the investigations of the Dirichlet forms associated with the underlying Markov chain driving the algorithms. For this purpose, we provide a detailed analysis on the error of the leapfrog integrator for Hamiltonian motions with both the kinetic and potential energy functions in general form. We characterize the explicit dependence of the convergence rates on key parameters such as the problem dimension, functional properties of both the target and auxiliary distributions, and the quality of the oracle.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 12 of its 30 references that are in the map. First posted on arXiv 21 May 2024.

Builds on

12 of 30 references.

References · 12

  1. 2019The Randomized Midpoint Method for Log-Concave Samplingcited by 78
  2. 2019Fast mixing of Metropolized Hamiltonian Monte Carlo: Benefits of multi-step gradientscited by 51
  3. 2018Coupling and Convergence for Hamiltonian Monte Carlocited by 36
  4. 2018Global Convergence of Stochastic Gradient Hamiltonian Monte Carlo for Non-Convex Stochastic Optimization: Non-Asymptotic Performance Bounds and Momentum-Based Accelerationcited by 31
  5. 2019Optimal Convergence Rate of Hamiltonian Monte Carlo for Strongly Logconcave Distributionscited by 28
  6. 2023When does Metropolized Hamiltonian Monte Carlo provably outperform Metropolis-adjusted Langevin algorithm?cited by 15
  7. 2018Dimensionally Tight Bounds for Second-Order Hamiltonian Monte Carlocited by 11
  8. 2022Unadjusted Hamiltonian MCMC with Stratified Monte Carlo Time Integrationcited by 8
  9. 2018Stochastic Gradient Hamiltonian Monte Carlo with Variance Reduction for Bayesian Inferencecited by 4
  10. 2021On Lq Convergence of the Hamiltonian Monte Carlocited by 1
  11. 2021HMC, an Algorithms in Data Mining, the Functional Analysis approachcited by 1
  12. 2021Hamiltonian Monte Carlo with Asymmetrical Momentum Distributionscited by 1

Built on by

Not cited yet.