论文标题
在约束空间中用里曼尼亚汉密尔顿蒙特卡洛进行抽样
Sampling with Riemannian Hamiltonian Monte Carlo in a Constrained Space
论文作者
论文摘要
我们首次证明，在非常高的尺寸（超过100,000）的情况下，不良条件，非平滑，受约束的分布可以有效地进行采样，以$ \ textit {在实践中} $。我们的算法将约束纳入了Riemannian版本的汉密尔顿蒙特卡洛，并保持稀疏性。这使我们能够实现与平滑度和条件数字无关的混合速率。 在系统生物学和线性编程中的基准数据集上，我们的算法按数量级优于现有软件包。特别是，我们从最大的人类代谢网络（Recon3D）中实现了1,000倍的加速来进行抽样。我们的软件包已被整合到眼镜蛇工具箱中。
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.
