Adaptive importance sampling (AIS) methods provide a useful alternative to Markov Chain Monte Carlo (MCMC) algorithms for performing inference of intractable distributions. Population Monte Carlo (PMC) algorithms constitute a family of AIS approaches which adapt the proposal distributions iteratively to improve the approximation of the target distribution. Recent work in this area primarily focuses on ameliorating the proposal adaptation procedure for high-dimensional applications. However, most of the AIS algorithms use simple proposal distributions for sampling, which might be inadequate in exploring target distributions with intricate geometries. In this work, we construct expressive proposal distributions in the AIS framework using normalizing flow, an appealing approach for modeling complex distributions. We use an iterative parameter update rule to enhance the approximation of the target distribution. Numerical experiments show that in high-dimensional settings, the proposed algorithm offers significantly improved performance compared to the existing techniques.

翻译：自适应重要性采样（AIS）方法为针对难以处理的分布进行推断提供了马尔可夫链蒙特卡洛（MCMC）算法的一种实用替代方案。群体蒙特卡洛（PMC）算法是AIS方法的一个分支，它通过迭代调整提议分布来改进对目标分布的近似。该领域近期的工作主要集中于改进高维场景下的提议分布自适应流程。然而，大多数AIS算法采用简单的提议分布进行采样，这可能在探索具有复杂几何结构的目标分布时存在不足。本研究利用正则化流（一种建模复杂分布的有效方法）在AIS框架中构建表达力强的提议分布。我们采用迭代参数更新规则来增强对目标分布的近似能力。数值实验表明，在高维场景下，所提算法相比现有技术具有显著更优的性能。