Markov Chain Monte Carlo inference of target posterior distributions in machine learning is predominately conducted via Hamiltonian Monte Carlo and its variants. This is due to Hamiltonian Monte Carlo based samplers ability to suppress random-walk behaviour. As with other Markov Chain Monte Carlo methods, Hamiltonian Monte Carlo produces auto-correlated samples which results in high variance in the estimators, and low effective sample size rates in the generated samples. Adding antithetic sampling to Hamiltonian Monte Carlo has been previously shown to produce higher effective sample rates compared to vanilla Hamiltonian Monte Carlo. In this paper, we present new algorithms which are antithetic versions of Riemannian Manifold Hamiltonian Monte Carlo and Quantum-Inspired Hamiltonian Monte Carlo. The Riemannian Manifold Hamiltonian Monte Carlo algorithm improves on Hamiltonian Monte Carlo by taking into account the local geometry of the target, which is beneficial for target densities that may exhibit strong correlations in the parameters. Quantum-Inspired Hamiltonian Monte Carlo is based on quantum particles that can have random mass. Quantum-Inspired Hamiltonian Monte Carlo uses a random mass matrix which results in better sampling than Hamiltonian Monte Carlo on spiky and multi-modal distributions such as jump diffusion processes. The analysis is performed on jump diffusion process using real world financial market data, as well as on real world benchmark classification tasks using Bayesian logistic regression.

翻译：机器学习中目标远地点分布的图象的推论主要是通过汉密尔顿·蒙特卡洛及其变体进行的,这是因为汉密尔顿·蒙特卡洛的取样员有能力抑制随机行走的行为。与马可夫链-蒙特卡洛的其他方法一样,汉密尔顿·蒙特卡洛生产了与汽车有关的样品,造成估测器差异很大,而且所制样品的样本规模低。在汉密尔顿·蒙特卡洛添加了抗药性取样,以产生比范尼拉·汉密尔顿·蒙特卡洛(vanilla Hamiltonian Monterian Monte Carlo)更高的有效回归率。在本文中,我们提出了新的算法,这些算法是里曼尼西亚·曼尼特·汉密尔顿·蒙特卡洛(Hamilton Monate Carlo) 的反基因版本,与其他方法一样,汉密尔密尔顿·蒙特·卡洛(Hamiltonimet-Carlo) 制作了与自动的比量粒子颗粒式的模型模型, 利用了全球的滚动式滚动分析结果,作为全球的滚动模型,在Mirton-Carmodal-Carmodal 的滚动分析中进行了全球的滚动分析。