Browsing by Subject "Point processes"
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Item Open Access Modeling non-stationary dynamics of spatio-temporal sequences with self-organizing point process models(Bilkent University, 2021-06) Karaahmetoğlu, OğuzhanWe investigate the challenging problem of modeling the non-stationary dynam-ics of spatio-temporal sequences for prediction applications. Spatio-temporal se-quence modeling has critical real-life applications such as natural disaster, social, and criminal event prediction. Even though this problem has been thoroughly studied, many approaches do not address the non-stationarity and sparsity of the spatio-temporal sequences, which are frequently observed in real-life sequences. Here, we introduce a novel prediction algorithm that is capable of modeling non-stationarity in both time and space. Moreover, our algorithm can model both densely and sparsely populated sequences. We partition the spatial region with a decision tree, where each node of the tree corresponds to a subregion. We model the event occurrences in di˙erent subregions in space with individual but inter-acting point processes. Our algorithm can jointly optimize the partitioning tree and the interacting point processes through a gradient-based optimization. We compare our approach with statistical models, probabilistic approaches, and deep learning based approaches, and show that our model achieves the best forecasting performance on real-life datasets such as earthquake and criminal event records.Item Open Access Modeling of spatio-temporal hawkes processes with randomized kernels(IEEE, 2020) İlhan, Fatih; Kozat, Süleyman SerdarWe investigate spatio-temporal event analysis using point processes. Inferring the dynamics of event sequences spatio-temporally has many practical applications including crime prediction, social media analysis, and traffic forecasting. In particular, we focus on spatio-temporal Hawkes processes that are commonly used due to their capability to capture excitations between event occurrences. We introduce a novel inference framework based on randomized transformations and gradient descent to learn the process. We replace the spatial kernel calculations by randomized Fourier feature-based transformations. The introduced randomization by this representation provides flexibility while modeling the spatial excitation between events. Moreover, the system described by the process is expressed within closed-form in terms of scalable matrix operations. During the optimization, we use maximum likelihood estimation approach and gradient descent while properly handling positivity and orthonormality constraints. The experiment results show the improvements achieved by the introduced method in terms of fitting capability in synthetic and real-life datasets with respect to the conventional inference methods in the spatio-temporal Hawkes process literature. We also analyze the triggering interactions between event types and how their dynamics change in space and time through the interpretation of learned parameters.