We introduce Reflective Hamiltonian Monte Carlo (ReHMC), an HMC-based algorithm to sample from a log-concave distribution restricted to a convex body. The random walk is based on incorporating reflections to the Hamiltonian dynamics such that the support of the target density is the convex body. We develop an efficient open source implementation of ReHMC and perform an experimental study on various high-dimensional datasets. The experiments suggest that ReHMC outperforms Hit-and-Run and Coordinate-Hit-and-Run regarding the time it needs to produce an independent sample, introducing practical truncated sampling in thousands of dimensions.

我们介绍了反射哈密顿蒙特卡洛 (ReHMC)，这是一种基于 HMC 的算法，用于从限制在凸体上的对数凹分布中进行采样。随机游走基于对哈密顿动力学的反射，使得目标密度的支持是凸体。我们开发了 ReHMC 的高效开源实现，并对各种高维数据集进行了实验研究。实验表明，就生成独立样本所需的时间而言，ReHMC 优于 Hit-and-Run 和 Coordinate-Hit-and-Run，引入了数千个维度的实际截断采样。