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On L 𝔮 convergence of the Hamiltonian Monte Carlo

  • Soumyadip Ghosh , Yingdong Lu ORCID logo and Tomasz Nowicki ORCID logo EMAIL logo
Published/Copyright: November 24, 2022
Journal of Applied Analysis
From the journal Journal of Applied Analysis Volume 29 Issue 1

Abstract

We establish L 𝔮 convergence for Hamiltonian Monte Carlo (HMC) algorithms. More specifically, under mild conditions for the associated Hamiltonian motion, we show that the outputs of the algorithms converge (strongly for 2 ≤ 𝔮 < ∞ and weakly for 1 < 𝔮 < 2 ) to the desired target distribution. In addition, we establish a general convergence rate for an L 𝔮 convergence given a convergence rate at a specific q * , and apply this result to conclude geometric convergence in the Euclidean space for HMC with uniformly strongly logarithmic concave target and auxiliary distributions. We also present the results of experiments to illustrate convergence in L 𝔮 .

Keywords: Convergence; Hamiltonian Monte Carlo
MSC 2010: 65P10; 91G60; 62G07

References

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Received: 2022-09-17
Accepted: 2022-09-19
Published Online: 2022-11-24
Published in Print: 2023-06-01

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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  1. Frontmatter
  2. Heaviside function as an activation function
  3. Krylov solvability under perturbations of abstract inverse linear problems
  4. Existence of solutions for a three-point Hadamard fractional resonant boundary value problem
  5. Positive solutions to mixed fractional p-Laplacian boundary value problems
  6. Maximum number of limit cycles for generalized Kukles differential system
  7. Stabilization of a 1-D transmission problem for the Rayleigh beam and string with localized frictional damping
  8. Certain multiplier results on Bp spaces
  9. Remarks on the Belitskii–Lyubich and discrete Markus–Yamabe conjectures
  10. On deferred statistical convergence of complex uncertain sequences
  11. Local existence and uniqueness of regular solutions to a Landau–Lifshitz–Bloch equation with applied current
  12. Converse Ohlin’s lemma for convex and strongly convex functions
  13. Approximate controllability results in α-norm for some partial functional integrodifferential equations with nonlocal initial conditions in Banach spaces
  14. Direct proofs of intrinsic properties of prox-regular sets in Hilbert spaces
  15. On the continuity properties of the Lp balls
  16. On L 𝔮 convergence of the Hamiltonian Monte Carlo
  17. Radii of starlikeness and convexity of generalized k-Bessel functions
  18. An iterative technique for solving split equality monotone variational inclusion and fixed point problems
https://doi.org/10.1515/jaa-2022-1006
Keywords for this article
Convergence; Hamiltonian Monte Carlo

Articles in the same Issue

  1. Frontmatter
  2. Heaviside function as an activation function
  3. Krylov solvability under perturbations of abstract inverse linear problems
  4. Existence of solutions for a three-point Hadamard fractional resonant boundary value problem
  5. Positive solutions to mixed fractional p-Laplacian boundary value problems
  6. Maximum number of limit cycles for generalized Kukles differential system
  7. Stabilization of a 1-D transmission problem for the Rayleigh beam and string with localized frictional damping
  8. Certain multiplier results on Bp spaces
  9. Remarks on the Belitskii–Lyubich and discrete Markus–Yamabe conjectures
  10. On deferred statistical convergence of complex uncertain sequences
  11. Local existence and uniqueness of regular solutions to a Landau–Lifshitz–Bloch equation with applied current
  12. Converse Ohlin’s lemma for convex and strongly convex functions
  13. Approximate controllability results in α-norm for some partial functional integrodifferential equations with nonlocal initial conditions in Banach spaces
  14. Direct proofs of intrinsic properties of prox-regular sets in Hilbert spaces
  15. On the continuity properties of the Lp balls
  16. On L 𝔮 convergence of the Hamiltonian Monte Carlo
  17. Radii of starlikeness and convexity of generalized k-Bessel functions
  18. An iterative technique for solving split equality monotone variational inclusion and fixed point problems
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