Graphical model based spatio-temporal modeling of extreme events

• Main Author: Zhang, Liaofan
• Other Authors: Justin Dauwels
• Format: Final Year Project
• Language: English
• Published: 2013
• Subjects: DRNTU::Engineering::Mathematics and analysis
• Online Access: http://hdl.handle.net/10356/54522
• Institution: Nanyang Technological University

A novel model is proposed in this thesis to describe in a flexible manner the extreme events in both spatial and temporal domain. This model can be used to model the occurrence of extreme events in different places and at different times. The model is based on the assumption that the block maximum (e.g. monthly or annually maximum) at each location and time instant follow a Generalized Extreme Value (GEV) distribution. The GEV parameters are then coupled together using a monoscale thin-membrane model across the space and a multiscale model across the time domain. Efficient inference algorithm has been proposed based on the framework of smoothing based optimization. In each loop of the optimization process, the GEV marginals are approximated by Gaussian unary potential function. The resulting problem can be simplified as a Gaussian graphical model inference problem and therefore embedded subgraph algorithm can be used to infer the marginal mean while low-rank approximation algorithm to learn the marginal variance. Synthetic and real data test are carried out to verify the accuracy and usefulness of the proposed model. Our results show that the importance of modeling extreme events in spatio-temporal domain, and demonstrate that the proposed model is a powerful tool for extreme events analysis as well.