论文标题
微型典型的哈密顿蒙特卡洛
Microcanonical Hamiltonian Monte Carlo
论文作者
论文摘要
与哈密顿蒙特卡罗（HMC）相反，我们开发了遵循固定能量汉密尔顿动力学的一类模型，这是一类遵循固定能量的模型，与哈密顿蒙特卡洛（HMC）相比，该模型遵循不同能量水平的规范分布。 MCHMC调整了汉密尔顿功能，使得在动量变量上恒定能量表面上的均匀分布的边际可得出所需的目标分布。我们表明，MCHMC需要偶尔能节能的能量来保存台球样的动量，以弹跳，类似于在HMC中的动量重采样。我们将弹跳的概念推广到一个连续版本，并在每个步骤中都保留了部分方向，从而使能量保存在阻尼不足的Langevin样动力学中，具有非高斯噪声（MCLMC）。 MCHMC和MCLMC具有条件数和维度的有利量表。我们开发了一种有效的高参数调整方案，该方案可实现高性能，并且在某些情况下，在几个标准基准问题上的螺母始终超过了HMC，而不仅仅是一个数量级。
We develop Microcanonical Hamiltonian Monte Carlo (MCHMC), a class of models which follow a fixed energy Hamiltonian dynamics, in contrast to Hamiltonian Monte Carlo (HMC), which follows canonical distribution with different energy levels. MCHMC tunes the Hamiltonian function such that the marginal of the uniform distribution on the constant-energy-surface over the momentum variables gives the desired target distribution. We show that MCHMC requires occasional energy conserving billiard-like momentum bounces for ergodicity, analogous to momentum resampling in HMC. We generalize the concept of bounces to a continuous version with partial direction preserving bounces at every step, which gives an energy conserving underdamped Langevin-like dynamics with non-Gaussian noise (MCLMC). MCHMC and MCLMC exhibit favorable scalings with condition number and dimensionality. We develop an efficient hyperparameter tuning scheme that achieves high performance and consistently outperforms NUTS HMC on several standard benchmark problems, in some cases by more than an order of magnitude.
