论文标题
使用保守的哈密顿蒙特卡洛（Hamiltonian Carlo），改善高维分布的采样功效
Improving sampling efficacy on high dimensional distributions with thin high density regions using Conservative Hamiltonian Monte Carlo
论文作者
论文摘要
汉密尔顿蒙特卡洛（Hamiltonian Monte Carlo）是马尔可夫链蒙特卡洛算法，它在许多应用中使用象征性积分器来从高维目标分布中进行样品，例如统计力学，贝叶斯统计和生成模型。但是，这样的分布往往具有较薄的高密度区域，这对符号积分器构成了巨大的挑战，即保持高接收概率所需的小能量误差。取而代之的是，我们提出了一种称为保守的汉密尔顿蒙特卡洛（Monte Carlo）的变体，使用$ r $ - 可逆的能量披露积分器来保留高接收概率。我们表明，我们的算法可以实现近似平稳性，而通过雅各布的雅各比式近似值确定了能量保存提案图的误差。数值证据表明，高密度区域和高维度的目标分布上的整合参数上的收敛性和鲁棒性提高了。此外，我们的算法版本也可以应用于目标分布的情况下，而无需梯度信息。
Hamiltonian Monte Carlo is a prominent Markov Chain Monte Carlo algorithm, which employs symplectic integrators to sample from high dimensional target distributions in many applications, such as statistical mechanics, Bayesian statistics and generative models. However, such distributions tend to have thin high density regions, posing a significant challenge for symplectic integrators to maintain the small energy errors needed for a high acceptance probability. Instead, we propose a variant called Conservative Hamiltonian Monte Carlo, using $R$--reversible energy-preserving integrators to retain a high acceptance probability. We show our algorithm can achieve approximate stationarity with an error determined by the Jacobian approximation of the energy-preserving proposal map. Numerical evidence shows improved convergence and robustness over integration parameters on target distributions with thin high density regions and in high dimensions. Moreover, a version of our algorithm can also be applied to target distributions without gradient information.
