Sampling with Riemannian Hamiltonian Monte Carlo in a Constrained Space
Sampling with Riemannian Hamiltonian Monte Carlo in a Constrained Space
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发表时间：
2022-02
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通讯作者：
Yunbum Kook;Y. Lee;Ruoqi Shen;S. Vempala
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作者：
Yunbum Kook;Y. Lee;Ruoqi Shen;S. Vempala
我们首次证明了病态的，非光滑的，约束分布在非常高的维度，超过100，000，可以有效地采样$\texit {in practice}$。我们的算法将限制纳入到黎曼版本的哈密顿蒙特卡罗，并保持稀疏性。这使我们能够实现独立于平滑度和条件数的混合速率。在系统生物学和线性规划的基准数据集上，我们的算法的性能优于现有的软件包的数量级。特别是，我们实现了1,000倍的采样速度从最大的已发表的人类代谢网络（RECON 3D）。我们的软件包已被纳入COBRA工具箱。
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.