We propose a new framework for efficiently sampling from complex probability distributions using a combination of normalizing flows and elliptical slice sampling (Murray et al., 2010). The central idea is to learn a diffeomorphism, through normalizing flows, that maps the non-Gaussian structure of the target distribution to an approximately Gaussian distribution. We then use the elliptical slice sampler, an efficient and tuning-free Markov chain Monte Carlo (MCMC) algorithm, to sample from the transformed distribution. The samples are then pulled back using the inverse normalizing flow, yielding samples that approximate the stationary target distribution of interest. Our transport elliptical slice sampler (TESS) is optimized for modern computer architectures, where its adaptation mechanism utilizes parallel cores to rapidly run multiple Markov chains for a few iterations. Numerical demonstrations show that TESS produces Monte Carlo samples from the target distribution with lower autocorrelation compared to non-transformed samplers, and demonstrates significant improvements in efficiency when compared to gradient-based proposals designed for parallel computer architectures, given a flexible enough diffeomorphism.

翻译：我们提出了一个新的框架，通过正态化流和椭圆片段抽样（Murray et al。，2010）的组合，高效地从复杂概率分布中采样。其核心思想是通过正态化流学习一个微分同胚，将目标分布的非高斯结构映射到一个近似高斯分布中。然后利用椭圆片段抽样器，一种高效的无调整马尔科夫链蒙特卡罗算法，从转换分布进行抽样。然后使用反向正态化流拉回样本，产生逼近感兴趣的稳态目标分布的样本。我们的交通椭圆片段抽样器（TESS）针对现代计算机体系结构进行了优化，其中其适应机制利用并行内核快速运行多个马尔科夫链进行几次迭代。数值演示表明，与非变换采样器相比，TESS从目标分布产生的蒙特卡罗样本具有更低的自相关性，并且在灵活的微分同胚的情况下，相比为并行计算机体系结构设计的基于梯度的提议，它展示了显着的效率改进。