论文标题
减少拒绝指数改善马尔可夫链蒙特卡洛抽样
Reducing rejection exponentially improves Markov chain Monte Carlo sampling
论文作者
论文摘要
过渡内核的选择严重影响了马尔可夫链蒙特卡洛法的性能。尽管选择内核很重要，但尚未确定最佳内核的指导原则。在这里，我们提出了一个单参数排斥控制过渡内核，可以应用于各种蒙特卡洛采样，并证明拒绝过程在确定采样效率方面起着重要作用。改变拒绝概率，我们检查了二维铁磁POTTS模型中订单参数的自相关时间。我们的结果表明，降低排斥率会导致在顺序自旋更新中自相关时间的指数减少，并且在随机自旋更新中的代数降低。常规算法的自相关时间几乎落在单个曲线上，这是拒绝率的函数。具有最佳参数的当前过渡内核为离散变量的一般情况提供了最有效的采样器之一。
The choice of transition kernel critically influences the performance of the Markov chain Monte Carlo method. Despite the importance of kernel choice, guiding principles for optimal kernels have not been established. Here, we propose a one-parameter rejection control transition kernel that can be applied to various Monte Carlo samplings and demonstrate that the rejection process plays a major role in determining the sampling efficiency. Varying the rejection probability, we examine the autocorrelation time of the order parameter in the two- and three-dimensional ferromagnetic Potts models. Our results reveal that reducing the rejection rate leads to an exponential decrease in autocorrelation time in sequential spin updates and an algebraic reduction in random spin updates. The autocorrelation times of conventional algorithms almost fall on a single curve as a function of the rejection rate. The present transition kernel with an optimal parameter provides one of the most efficient samplers for general cases of discrete variables.
