Sampling from a complex distribution $\pi$ and approximating its intractable normalizing constant Z are challenging problems. In this paper, a novel family of importance samplers (IS) and Markov chain Monte Carlo (MCMC) samplers is derived. Given an invertible map T, these schemes combine (with weights) elements from the forward and backward Orbits through points sampled from a proposal distribution $\rho$. The map T does not leave the target $\pi$ invariant, hence the name NEO, standing for Non-Equilibrium Orbits. NEO-IS provides unbiased estimators of the normalizing constant and self-normalized IS estimators of expectations under $\pi$ while NEO-MCMC combines multiple NEO-IS estimates of the normalizing constant and an iterated sampling-importance resampling mechanism to sample from $\pi$. For T chosen as a discrete-time integrator of a conformal Hamiltonian system, NEO-IS achieves state-of-the art performance on difficult benchmarks and NEO-MCMC is able to explore highly multimodal targets. Additionally, we provide detailed theoretical results for both methods. In particular, we show that NEO-MCMC is uniformly geometrically ergodic and establish explicit mixing time estimates under mild conditions.
翻译:在本文中,由重要取样员(IS)和马尔科夫链-蒙特卡洛(MCMCC)取样员组成的新组合得出了一个重要取样员(IS)和马克夫-连锁-蒙特卡洛(MCMC)取样员组成的新组合。考虑到不可逆的地图T,这些计划将前轨道和后轨道的(加权)元素(通过从建议分发中抽取的点($rho$)结合到从前轨道和后轨道的样本(加权)元素(加权)。地图T没有留下目标(1美元),因此没有留下目标(1美元)变化,因此没有留下名称为非平衡轨道的近地物体。近地物体-IS提供了标准化的常态和自我规范的定时和自我规范的定时评估员。 近地物体-监控中心提供了对常态和反复的采样再采样机制的多重估计值(加权),从$\rho美元进行取样。对于被选择为符合要求的汉密尔顿系统离散时间聚合器的近地标,近地-IS在困难的基准基准线上的状态下提供了艺术表现。近地点-监控监测中心-MC能够对高模模型进行精确的精确的精确分析。