相关论文: Adaptive Step Size for Hybrid Monte Carlo Algorith…

Hamiltonian Monte Carlo can provide powerful inference in complex statistical problems, but ultimately its performance is sensitive to various tuning parameters. In this paper we use the underlying geometry of Hamiltonian Monte Carlo to…

Three possibilities to speed up the Hybrid Monte Carlo algorithm are investigated. Changing the step-size adaptively brings no practical gain. On the other hand, substantial improvements result from using an approximate Hamiltonian or a…

Traditional step size controllers make the tacit assumption that the cost of a time step is independent of the step size. This is reasonable for explicit and implicit integrators that use direct solvers. In the context of exponential…

It has been known for a long time that stratification is one possible strategy to obtain higher convergence rates for the Monte Carlo estimation of integrals over the hyper-cube $[0, 1]^s$ of dimension $s$. However, stratified estimators…

We construct numerical integrators for Hamiltonian problems that may advantageously replace the standard Verlet time-stepper within Hybrid Monte Carlo and related simulations. Past attempts have often aimed at boosting the order of accuracy…

The automatic selection of an appropriate time step size has been considered extensively in the literature. However, most of the strategies developed operate under the assumption that the computational cost (per time step) is independent of…

We study the feature-scaled version of the Monte Carlo algorithm with linear function approximation. This algorithm converges to a scale-invariant solution, which is not unduly affected by states having feature vectors with large norms. The…

In this paper, we aim to compute numerical approximation integral by using an adaptive Monte Carlo algorithm. We propose a stratified sampling algorithm based on an iterative method which splits the strata following some quantities called…

In this paper, we propose an adaptive step size strategy for a class of line search methods for orthogonality constrained minimization problems, which avoids the classic backtracking procedure. We prove the convergence of the line search…

Monte Carlo (MC) methods for numerical integration seem to be embarassingly parallel on first sight. When adaptive schemes are applied in order to enhance convergence however, the seemingly most natural way of replicating the whole job on…

While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…

We propose an adaptive importance sampling scheme for Gaussian approximations of intractable posteriors. Optimization-based approximations like variational inference can be too inaccurate while existing Monte Carlo methods can be too slow.…

Adaptive stepsize control is a critical feature for the robust and efficient numerical solution of initial-value problems in ordinary differential equations. In this paper, we show that adaptive stepsize control can be incorporated within a…

Monte Carlo integration is a commonly used technique to compute intractable integrals and is typically thought to perform poorly for very high-dimensional integrals. To show that this is not always the case, we examine Monte Carlo…

In this paper we address the widely-experienced difficulty in tuning Hamiltonian-based Monte Carlo samplers. We develop an algorithm that allows for the adaptation of Hamiltonian and Riemann manifold Hamiltonian Monte Carlo samplers using…

This paper surveys in detail the relations between numerical integration and the Hamiltonian (or hybrid) Monte Carlo method (HMC). Since the computational cost of HMC mainly lies in the numerical integrations, these should be performed as…

Many common Markov chain Monte Carlo (MCMC) kernels can be formulated using a deterministic involutive proposal with a step size parameter. Selecting an appropriate step size is often a challenging task in practice; and for complex…

Hybrid Monte Carlo (HMC) generates samples from a prescribed probability distribution in a configuration space by simulating Hamiltonian dynamics, followed by the Metropolis (-Hastings) acceptance/rejection step. Compressible HMC (CHMC)…

One of the most demanding calculations is to generate random samples from a specified probability distribution (usually with an unknown normalizing prefactor) in a high-dimensional configuration space. One often has to resort to using a…

Science and engineering problems subject to uncertainty are frequently both computationally expensive and feature nonsmooth parameter dependence, making standard Monte Carlo too slow, and excluding efficient use of accelerated uncertainty…