Robust Inference Based On the Complementary Hamiltonian Monte Carlo

Xu, Xiaopeng; Liu, Chuancai; Yang, Hongji

doi:10.1109/tr.2021.3117189

Cited by 4 publications

(3 citation statements)

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“…As a result, ∂K/∂q might be omitted or simplified in practice [13]. Ignoring the term, on the other hand, may result in systematic errors for single-trajectory algorithms that utilize non-physical kinetic energy [7].…”

Section: (28)mentioning

confidence: 99%

“…The suggested single or multi-trajectory algorithm is analogous to the alternating two-trajectory algorithm [7]. By incorporating N distinct types of trajectories, both H and δ will be N-dimensional arrays, as each trajectory needs adjust its own total energy and step size.…”

Section: Algorithm Descriptionmentioning

confidence: 99%

“…If the total energy of a single-particle system is conserved, the mutual proposal (jump) probability between two terminals of a trajectory are equal [7]. Due to the fact that limiting the total energy of single-particle systems will limit exploration significantly, multi-particle systems with collision effect can be used to reconcile exploration and stability.…”

Section: Introductionmentioning

confidence: 99%

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A Multi-Trajectory Monte Carlo Sampler

Xu¹,

Xu²,

Liu³

et al. 2022

Journal of Internet Technology

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<p>Markov Chain Monte Carlo techniques based on Hamiltonian dynamics can sample the first or last principal components of multivariate probability models using simulated trajectories. However, when components’ scales span orders of magnitude, these approaches may be unable of accessing all components adequately. While it is possible to reconcile the first and last components by alternating between two different types of trajectories, the sampling of intermediate components may be imprecise. In this paper, a function generalizing the kinetic energies of Hamiltonian Monte Carlo and Riemannian Manifold Hamiltonian Monte Carlo is proposed, and it is found that the methods based on a specific form of the function can more accurately sample normal distributions. Additionally, the multi-particle algorithm’s reasoning is given after a review of some statistical ideas.</p> <p> </p>

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Section: (28)mentioning

confidence: 99%

Section: Algorithm Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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