Different spatial point process models and techniques have been developed in the past decades to facilitate the statistical analysis of spatial point patterns. However, in some cases the spatial point process methodology is scarce and no flexible models nor suitable statistical methods are available. For example, due to its complexity, the statistical analysis of spatial point patterns of several groups observed at a number of time instances has not been studied in-depth, and there are a few limited models and methods available for such data. In the present work, we provide a mathematical framework for coupling neural network methods with the statistical analysis of point patterns. In particular, we discuss an example of deep neural networks in the statistical analysis of highly multivariate spatial point patterns and provide a new strategy for building spatio-temporal point processes using variational autoencoder generative neural networks.

在过去的几十年中，已经开发了不同的空间点过程模型和技术，以促进空间点模式的统计分析。然而，在某些情况下，空间点处理方法是稀缺的，既没有灵活的模型，也没有合适的统计方法。例如，由于其复杂性，在多个时间实例中观察到的几个组的空间点模式的统计分析尚未得到深入研究，并且有一些有限的模型和方法可用于此类数据。在目前的工作中，我们提供了一个数学框架，用于将神经网络方法与点模式的统计分析相结合。特别是，