Neyman-Scott processes (NSPs) have been applied across a range of fields to model points or temporal events with a hierarchy of clusters. Markov chain Monte Carlo (MCMC) is typically used for posterior sampling in the model. However, MCMC's mixing time can cause the resulting inference to be slow, and thereby slow down model learning and prediction. We develop the first variational inference (VI) algorithm for NSPs, and give two examples of suitable variational posterior point process distributions. Our method minimizes the inclusive Kullback-Leibler (KL) divergence for VI to obtain the variational parameters. We generate samples from the approximate posterior point processes much faster than MCMC, as we can directly estimate the approximate posterior point processes without any MCMC steps or gradient descent. We include synthetic and real-world data experiments that demonstrate our VI algorithm achieves better prediction performance than MCMC when computational time is limited.

翻译：内曼-斯科特过程（NSPs）在多个领域中被应用于对具有层级聚类结构的点或时间事件进行建模。该模型通常采用马尔可夫链蒙特卡洛（MCMC）方法进行后验采样。然而，MCMC的混合时间可能导致推断速度缓慢，进而影响模型学习与预测效率。我们首次提出了针对NSPs的变分推断（VI）算法，并给出了两种合适的变分后验点过程分布实例。该方法通过最小化包含性KL散度来获取变分参数。由于可直接估计近似后验点过程而无需任何MCMC步骤或梯度下降，我们从近似后验点过程中生成样本的速度远快于MCMC。合成数据集与实际数据集的实验表明，当计算时间受限时，我们的VI算法比MCMC具有更优的预测性能。