论文标题
轨道MCMC
Orbital MCMC
论文作者
论文摘要
马尔可夫链蒙特卡洛（MCMC）算法普遍使用复杂的确定性转换来生成提议点，然后通过大都市杂货店（MHG）测试对其进行过滤。但是，目标度量不变性的条件对这些转换的设计构成了限制。在本文中，我们首先考虑了随机马尔可夫内核的接受测试，以任意确定性地图为提案生成器。当使用第二个周期（互动）的轨道应用于转换时，该测试将减少为MHG测试。基于派生的测试，我们提出了两种实际算法：一种是通过从任何差异形态中构建周期性轨道来运行的，另一个是关于状态空间（例如优化轨迹）的另一个轨道。最后，我们进行了一项实证研究，证明了两个内核的实际优势。
Markov Chain Monte Carlo (MCMC) algorithms ubiquitously employ complex deterministic transformations to generate proposal points that are then filtered by the Metropolis-Hastings-Green (MHG) test. However, the condition of the target measure invariance puts restrictions on the design of these transformations. In this paper, we first derive the acceptance test for the stochastic Markov kernel considering arbitrary deterministic maps as proposal generators. When applied to the transformations with orbits of period two (involutions), the test reduces to the MHG test. Based on the derived test we propose two practical algorithms: one operates by constructing periodic orbits from any diffeomorphism, another on contractions of the state space (such as optimization trajectories). Finally, we perform an empirical study demonstrating the practical advantages of both kernels.
