Normalizing flows can generate complex target distributions and thus show promise in many applications in Bayesian statistics as an alternative or complement to MCMC for sampling posteriors. Since no data set from the target posterior distribution is available beforehand, the flow is typically trained using the reverse Kullback-Leibler (KL) divergence that only requires samples from a base distribution. This strategy may perform poorly when the posterior is complicated and hard to sample with an untrained normalizing flow. Here we explore a distinct training strategy, using the direct KL divergence as loss, in which samples from the posterior are generated by (i) assisting a local MCMC algorithm on the posterior with a normalizing flow to accelerate its mixing rate and (ii) using the data generated this way to train the flow. The method only requires a limited amount of \textit{a~priori} input about the posterior, and can be used to estimate the evidence required for model validation, as we illustrate on examples.

翻译：由于事先没有来自目标后继分布的数据集,因此通常使用Kullback-Leibler(KL)的逆向差异来培训流动,这种差异只需要从基分布中提取样本。当后继值复杂,难以用未经训练的正常流进行取样时,这一战略可能效果不佳。在这里,我们探索了一种不同的培训战略,使用直接的 KL 差异作为损失,从后继值生成样本,其方法是(一) 协助在后继值上进行本地的 MMC 算法,使其正常化,以加速其混合速度,(二) 利用由此生成的数据来培训流动。该方法只需要有限的数量 \ textit{a~ priori} 有关后继值的输入,并且可以用来估计模型验证所需的证据,正如我们举例说明的那样。