UCLA

Many accurate spatiotemporal data sets have recently become available for research. Real-world applications create strong demands for a better multivariate point-process modeling. In this thesis, we develop new multivariate models with generalization ability and scalability.

The first two chapters provide a research background, real-world problems and a mathematical introduction to point-process models.

In chapter 3, we develop a nonparametric method for multivariate spatiotemporal Hawkes processes with applications on network reconstruction. In contrast to prior work, which has often focused on exclusively temporal information, our approach uses spatiotemporal information and does not assume a specific parametric form. Our results demonstrate that, in comparison to using only temporal data, our approach yields improved network reconstruction, providing a basis for meaningful subsequent analysis---such as examinations of community structure and motifs---of the reconstructed networks.

In chapter 4, we present a fast and accurate estimation method for multivariate Hawkes processes. Our method, with guaranteed consistency, combines two estimation approaches. Extensive numerical experiments, with synthetic data and real-world social network data, show that our method improves the accuracy, scalability and computational efficiency of prevailing estimation approaches. Moreover, it greatly boosts the performance of Hawkes process-based models on social network reconstruction and helps to understand the spatiotemporal triggering dynamics over social media.

In chapter 5, we focus on multivariate spatial point processes, which can describe heterotopic data over space. However, highly multivariate intensities are computationally challenging due to the curse of dimensionality. To bridge this gap, we introduce a declustering-based hidden-variable model that leads to an efficient inference via a variational autoencoder (VAE). We also prove that this model is a generalization of the VAE-based model for collaborative filtering. This leads to an interesting application of spatial point-process models to recommender systems. Experimental results show the method's utility on both synthetic data and real-world data.

Finally, in chapter 6, we show how multivariate point processes can be applied to opioid overdose events and real-time prediction of the hourly crime rate. In chapter 7, we discuss future directions and conclude the thesis.