We introduce Reflective Hamiltonian Monte Carlo (ReHMC), an HMC-based algorithm, to sample from a log-concave distribution restricted to a convex body. We prove that, starting from a warm start, the walk mixes to a log-concave target distribution $\pi(x) \propto e^{-f(x)}$, where $f$ is $L$-smooth and $m$-strongly-convex, within accuracy $\varepsilon$ after $\widetilde O(\kappa d^2 \ell^2 \log (1 / \varepsilon))$ steps for a well-rounded convex body where $\kappa = L / m$ is the condition number of the negative log-density, $d$ is the dimension, $\ell$ is an upper bound on the number of reflections, and $\varepsilon$ is the accuracy parameter. We also developed an efficient open source implementation of ReHMC and we performed an experimental study on various high-dimensional data-sets. The experiments suggest that ReHMC outperfroms Hit-and-Run and Coordinate-Hit-and-Run regarding the time it needs to produce an independent sample and introduces practical truncated sampling in thousands of dimensions.

翻译：我们引入了反射的汉密尔顿蒙特卡洛(ReHMC)算法(ReHMC ), 用于从限于卷心体的对数组合分布样本。 我们证明,从一个温暖的开端开始,行走混合到一个对数组合目标分布$\pi(x)\ propto e ⁇ -f(x)}$(美元,美元是负日志密度的条件号,美元是反射次数的上限,美元是反射次数的精度上限,美元是精确度参数。 我们还开发了REMC高效的开放源实施,我们从高分辨率和高分辨率取样到高分辨率数据模型的实验性实验性研究。