Probabilistic Deep Learning for Highly Multivariate Spatio-Temporal Log-Gaussian Cox Processes

Multivariate point patterns have become increasingly common due to the advancement of technology for massive data collection. Parameter estimation is vital for understanding the distributional patterns within such data. However, performing estimation using a parametric approach on multivariate point pattern data is challenging due to the curse of dimensionality, making parametric estimation increasingly difficult as data dimensionality grows. Deep learning offers a promising alternative due to its ability to model complex nonlinear patterns in large datasets. Despite limited applications in multivariate point pattern analysis, this study aims to use deep learning as a tool for parameter estimation of the multivariate log-Gaussian Cox Process (LGCP) model. We employ the concept of probabilistic deep learning, ensuring that each estimated parameter follows a certain distribution that aligns with its assumption. We assess our model performance via a simulation study, and analyze the highly multivariate spatio-temporal point pattern data of Barro Colorado Island (BCI). Both the simulation study and application demonstrate our model effectiveness over previous approaches to handle highly multivariate point pattern data.