We demonstrate for the first time that ill-conditioned, non-smooth, constrained distributions in very high dimension, upwards of 100,000, can be sampled efficiently $\textit{in practice}$. Our algorithm incorporates constraints into the Riemannian version of Hamiltonian Monte Carlo and maintains sparsity. This allows us to achieve a mixing rate independent of smoothness and condition numbers. On benchmark data sets in systems biology and linear programming, our algorithm outperforms existing packages by orders of magnitude. In particular, we achieve a 1,000-fold speed-up for sampling from the largest published human metabolic network (RECON3D). Our package has been incorporated into the COBRA toolbox.

翻译：我们第一次证明,在非常高的维度(即10万美元以上)下,条件恶劣的、非悬浮的、受限制的分布可以高效地取样。我们的算法将限制纳入汉密尔顿·蒙特卡洛的里曼尼版并保持零散状态。这使我们能够实现一种不光滑和条件数字的混合率。在系统生物学和线性编程的基准数据集方面,我们的算法以数量级比现有包件要好。特别是,我们从最大的已出版的人类代谢网络(RECON3D)中实现1,000倍的取样速度。我们的软件包已经纳入COBRA工具箱。