论文标题
连接点：数值随机汉密尔顿蒙特卡洛与状态依赖的事件发生率
Connecting the Dots: Numerical Randomized Hamiltonian Monte Carlo with State-Dependent Event Rates
论文作者
论文摘要
引入了数值通用的随机汉密尔顿蒙特卡洛，作为一种可靠，易于使用和计算快速替代的传统马尔可夫链蒙特卡洛方法，用于连续目标分布。通过允许依赖状态依赖的事件速率来概括随机HMC（Bou-Rabee和Sanz-Serna，2017年）的一系列分段确定性Markov过程。在非常温和的限制下，此类过程将具有所需的目标分布作为不变分布。其次，考虑了基于二阶普通微分方程（ODE）的自适应数值集成此类过程的数值实现。数值实现产生了一种大致但高度可靠的算法，与传统的汉密尔顿蒙特卡洛不同，它可以利用完整的哈密顿轨迹（因此标题）。所提出的算法相对于相关的基准可能会产生较大的加速和稳定性的改善，而相对于整体蒙特卡洛误差而产生的数值偏见可忽略不计。授予访问高质量的ODE代码，即使是高度挑战和高维的目标分布，提出的方法既易于实施和使用。
Numerical Generalized Randomized Hamiltonian Monte Carlo is introduced, as a robust, easy to use and computationally fast alternative to conventional Markov chain Monte Carlo methods for continuous target distributions. A wide class of piecewise deterministic Markov processes generalizing Randomized HMC (Bou-Rabee and Sanz-Serna, 2017) by allowing for state-dependent event rates is defined. Under very mild restrictions, such processes will have the desired target distribution as an invariant distribution. Secondly, the numerical implementation of such processes, based on adaptive numerical integration of second order ordinary differential equations (ODEs) is considered. The numerical implementation yields an approximate, yet highly robust algorithm that, unlike conventional Hamiltonian Monte Carlo, enables the exploitation of the complete Hamiltonian trajectories (hence the title). The proposed algorithm may yield large speedups and improvements in stability relative to relevant benchmarks, while incurring numerical biases that are negligible relative to the overall Monte Carlo errors. Granted access to a high-quality ODE code, the proposed methodology is both easy to implement and use, even for highly challenging and high-dimensional target distributions.
