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：我们提出了一种新框架，通过结合归一化流与椭圆切片采样（Murray 等，2010），高效地从复杂概率分布中采样。核心思想是利用归一化流学习一个微分同胚，将目标分布的非高斯结构映射为近似高斯分布。随后使用椭圆切片采样器（一种高效且无需调参的马尔可夫链蒙特卡洛（MCMC）算法）对变换后的分布进行采样。通过归一化流的逆映射拉回样本，从而获得近似服从目标平稳分布的样本。我们的运输椭圆切片采样器（TESS）针对现代计算机架构进行了优化，其自适应机制利用并行核心快速运行多条马尔可夫链（仅需少量迭代）。数值实验表明，与未变换的采样器相比，TESS 能从目标分布中生成自相关性更低的蒙特卡洛样本；当微分同胚具有足够灵活性时，相比专为并行计算机架构设计的基于梯度的提议机制，TESS 在效率上展现出显著提升。