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）方法为马尔可夫链蒙特卡洛（MCMC）算法处理难以解析分布的推断问题提供了有效替代方案。群体蒙特卡洛（PMC）算法作为AIS方法的一个分支，通过迭代调整提议分布来改进目标分布的逼近效果。该领域近期研究主要聚焦于优化适用于高维场景的提议分布自适应策略。然而，多数AIS算法采用简单提议分布进行采样，这种策略在探索具有复杂几何结构的目标分布时可能力有不逮。本研究在AIS框架下利用归一化流（normalizing flow）构建了具有表达能力的提议分布，该建模方法特别适用于复杂分布的表征。我们采用迭代参数更新规则来增强目标分布的逼近精度。数值实验表明，在高维场景下，与现有技术相比，本文提出的算法性能得到了显著提升。