Spatio-temporal point processes with deep non-stationary kernels

Point process data, consisting of sequential events with timestamps and associated information such as location or category, are ubiquitous in modern scientific fields and real-world applications. The distribution of events is of great scientific and practical interest, both for predicting new events and understanding the events' generative dynamics (Reinhart, 2018). To model such discrete events in continuous time and space, spatio-temporal point processes (STPPs) are widely used in a diverse range of domains, including modeling earthquakes (Ogata, 1988, 1998), the spread of infectious diseases (Schoenberg et al., 2019; Dong et al., 2021), and wildfire propagation Hering et al. (2009). A modeling challenge is to accurately capture the underlying generative model of event occurrence in general spatio-temporal point processes (STPP) while maintaining the model efficiency. Specific parametric forms of conditional intensity are proposed in seminal works of Hawkes process (Hawkes, 1971; Ogata, 1988) to tackle the issue of computational complexity in STPPs, which requires evaluating the complex multivariate integral in the likelihood function. They use an exponentially decaying influence kernel to measure the influence of a past event over time and assume the influence of all past events is positive and linearly additive. Despite computational simplicity (since the integral of the likelihood function is avoided), such a parametric form limits the model's practicality in modern applications. Recent models use neural networks in modeling point processes to capture complicated event occurrences. RNN (Du et al., 2016) and LSTM (Mei and Eisner, 2017) have been used by taking