In the last decade several sampling methods have been proposed which rely on piecewise deterministic Markov processes (PDMPs). PDMPs are based on following deterministic trajectories with stochastic events which correspond to jumps in the state space. We propose implementing constraints in this setting to exploit geometries of high-dimensional problems by introducing a PDMP version of Riemannian manifold Hamiltonian Monte Carlo, which we call randomized time Riemannian manifold Hamiltonian Monte Carlo. Efficient sampling on constrained spaces is also needed in many applications including protein conformation modelling, directional statistics and free energy computations. We will show how randomizing the duration parameter for Hamiltonian flow can improve the robustness of Riemannian manifold Hamiltonian Monte Carlo methods. We will then compare methods on some example distributions which arise in application and provide an application of sampling on manifolds in high-dimensional covariance estimation.
翻译:近十年来,人们提议采用几种采样方法,这些采样方法依赖于确定性马可夫工艺(PDMPs),而PDMPs则基于与州空间跳跃相对应的随机性随机性随机性轨迹。我们提议在这种环境中实施限制,以利用高维问题的地理特征,方法是采用里曼尼的多元汉密尔顿·蒙特卡洛的PDMP版本,我们称之为随机性时间,里曼尼安的多元汉密尔顿·蒙特卡洛。在许多应用中,包括蛋白分解模型、定向统计和自由能源计算,也需要对受限空间进行有效的采样。我们将展示汉密尔顿河流的随机性参数可以如何改善里曼尼汉密尔顿·蒙特卡洛的多元性方法的稳健性。然后我们将比较一些应用中出现的分布方法,并对高维可变性估计的多管进行采样。