Recent advances in machine learning have led to the development of new methods for enhancing Monte Carlo methods such as Markov chain Monte Carlo (MCMC) and importance sampling (IS). One such method is normalizing flows, which use a neural network to approximate a distribution by evaluating it pointwise. Normalizing flows have been shown to improve the performance of MCMC and IS. On the other side, (randomized) quasi-Monte Carlo methods are used to perform numerical integration. They replace the random sampling of Monte Carlo by a sequence which cover the hypercube more uniformly, resulting in better convergence rates for the error that plain Monte Carlo. In this work, we combine these two methods by using quasi-Monte Carlo to sample the initial distribution that is transported by the flow. We demonstrate through numerical experiments that this combination can lead to an estimator with significantly lower variance than if the flow was sampled with a classic Monte Carlo.

翻译：近年来机器学习的进展催生了多种增强蒙特卡洛方法（如马尔可夫链蒙特卡洛MCMC和重要性采样IS）的新技术。其中归一化流通过神经网络逐点评估来近似分布，已被证明能有效提升MCMC和IS的性能。另一方面，（随机化）拟蒙特卡洛方法通过采用比原始蒙特卡洛更均匀覆盖超立方体的序列替代随机采样进行数值积分，可获得更优的误差收敛速率。本研究将两者结合，利用拟蒙特卡洛方法对经归一化流变换的初始分布进行采样。数值实验表明，与经典蒙特卡洛采样归一化流相比，该组合方法能显著降低估计量的方差。