With the recently increased interest in probabilistic models, the efficiency of an underlying sampler becomes a crucial consideration. Hamiltonian Monte Carlo (HMC) is one popular option for models of this kind. Performance of the method, however, strongly relies on a choice of parameters associated with an integration for Hamiltonian equations. Up to date, such a choice remains mainly heuristic or introduces time complexity. We propose a novel computationally inexpensive and flexible approach (we call it Adaptive Tuning or ATune) that, by combining a theoretical analysis of the multivariate Gaussian model with simulation data generated during a burn-in stage of a HMC simulation, detects a system specific splitting integrator with a set of reliable sampler's hyperparameters, including their credible randomization intervals, to be readily used in a production simulation. The method automatically eliminates those values of simulation parameters which could cause undesired extreme scenarios, such as resonance artifacts, low accuracy or poor sampling. The new approach is implemented in the in-house software package HaiCS, with no computational overheads introduced in a production simulation, and can be easily incorporated in any package for Bayesian inference with HMC. The tests on popular statistical models reveal the superiority of adaptively tuned standard and generalized HMC (GHMC) methods in terms of stability, performance and accuracy over conventional HMC tuned heuristically and coupled with the well-established integrators. We also claim that GHMC is preferable for achieving high sampling performance. The efficiency of the new methodology is assessed in comparison with state-of-the-art samplers, e.g. NUTS, in real-world applications, such as endocrine therapy resistance in cancer, modeling of cell-cell adhesion dynamics and influenza A epidemic outbreak.

翻译：随着概率模型近期受到越来越多的关注，底层采样器的效率成为一个关键考量因素。哈密顿蒙特卡洛（HMC）是此类模型中一种常用的选择。然而，该方法的性能在很大程度上依赖于与哈密顿方程积分相关的参数选择。迄今为止，此类选择主要依赖于启发式方法或会引入时间复杂性。我们提出了一种新颖的计算成本低廉且灵活的方法（我们称之为自适应调参或ATune），该方法通过将多元高斯模型的理论分析与HMC模拟预热阶段生成的模拟数据相结合，检测出系统特定的分裂积分器及一组可靠的采样器超参数（包括其可信随机化区间），以便直接用于生产模拟。该方法自动剔除那些可能导致不良极端场景（如共振伪影、精度低下或采样效果差）的模拟参数值。新方法已在内部软件包HaiCS中实现，在生产模拟中不会引入额外的计算开销，并且可以轻松集成到任何使用HMC进行贝叶斯推断的软件包中。在经典统计模型上的测试表明，自适应调参的标准HMC及广义HMC（GHMC）方法在稳定性、性能和精度方面均优于采用启发式调参并结合成熟积分器的传统HMC。我们还指出，为实现高采样性能，GHMC是更优选择。通过与前沿采样器（如NUTS）在真实场景应用（如癌症内分泌治疗耐药性、细胞间粘附动力学建模和甲型流感疫情暴发）中的对比，评估了新方法的效率。