We propose Kernel Hamiltonian Monte Carlo (KMC), a gradient-free adaptive
MCMC algorithm based on Hamiltonian Monte Carlo (HMC). On target densities
where classical HMC is not an option due to intractable gradients, KMC
adaptively learns the target's gradient structure by fitting an exponential
family model in a Reproducing Kernel Hilbert Space. Computational costs are
reduced by two novel efficient approximations to this gradient. While being
asymptotically exact, KMC mimics HMC in terms of sampling efficiency, and
offers substantial mixing improvements over state-of-the-art gradient free
samplers. We support our claims with experimental studies on both toy and
real-world applications, including Approximate Bayesian Computation and
exact-approximate MCMC.

本研究提出了核哈密顿蒙特卡罗算法（KMC）, 一种基于哈密顿蒙特卡罗的无梯度自适应 MCMC 算法。在目标密度函数不可求梯度时，KMC 通过拟合重现核希尔伯特空间中的指数族模型，自适应地学习目标的梯度结构。其具有收敛到精确解的能力，且在采样效率上与 HMC 相当并且具有极大的混合改进，通过玩具和现实应用的实验研究来支持我们的结论，包括近似贝叶斯计算和精确 - 近似 MCMC。