Long Term Predictive Modeling on Big Spatio-Temporal Data

In the era of massive data, one of the most promising research fields involves the analysis of large-scale Spatio-temporal databases to discover exciting and previously unknown but potentially useful patterns from data collected over time and space. A modeling process in this domain must take temporal and spatial correlations into account, but with the dimensionality of the time and space measurements increasing, the number of elements potentially contributing to a target sharply grows, making the target\u27s long-term behavior highly complex, chaotic, highly dynamic, and hard to predict. Therefore, two different considerations are taken into account in this work: one is about how to identify the most relevant and meaningful features from the original Spatio-temporal feature space; the other is about how to model complex space-time dynamics with sensitive dependence on initial and boundary conditions. First, identifying strongly related features and removing the irrelevant or less important features with respect to a target feature from large-scale Spatio-temporal data sets is a critical and challenging issue in many fields, including the evolutionary history of crime hot spots, uncovering weather patterns, predicting floodings, earthquakes, and hurricanes, and determining global warming trends. The optimal sub-feature-set that contains all the valuable information is called the Markov Boundary. Unfortunately, the existing feature selection methods often focus on identifying a single Markov Boundary when real-world data could have many feature subsets that are equally good boundaries. In our work, we design a new multiple-Markov-boundary-based predictive model, Galaxy, to identify the precursors to heavy precipitation event clusters and predict heavy rainfall with a long lead time. We applied Galaxy to an extremely high-dimensional meteorological data set and finally determined 15 Markov boundaries related to heavy rainfall events in the Des Moines River Basin in Iowa. Our model identified the cold surges along the coast of Asia as an essential precursor to the surface weather over the United States, a finding which was later corroborated by climate experts. Second, chaotic behavior exists in many nonlinear Spatio-temporal systems, such as climate dynamics, weather prediction, and the space-time dynamics of virus spread. A reliable solution for these systems must handle their complex space-time dynamics and sensitive dependence on initial and boundary conditions. Deep neural networks\u27 hierarchical feature learning capabilities in both spatial and temporal domains are helpful for nonlinear Spatio-temporal dynamics modeling. However, sensitive dependence on initial and boundary conditions is still challenging for theoretical research and many critical applications. This study proposes a new recurrent architecture, error trajectory tracing, and accompanying training regime, Horizon Forcing, for prediction in chaotic systems. These methods have been validated on real-world Spatio-temporal data sets, including one meteorological dataset, three classics, chaotic systems, and four real-world time series prediction tasks with chaotic characteristics. Experiments\u27 results show that each proposed model could outperform the performance of current baseline approaches

The Effects of Evolutionary Adaptations on Spreading Processes in Complex Networks

A common theme among the proposed models for network epidemics is the assumption that the propagating object, i.e., a virus or a piece of information, is transferred across the nodes without going through any modification or evolution. However, in real-life spreading processes, pathogens often evolve in response to changing environments and medical interventions and information is often modified by individuals before being forwarded. In this paper, we investigate the evolution of spreading processes on complex networks with the aim of i) revealing the role of evolution on the threshold, probability, and final size of epidemics; and ii) exploring the interplay between the structural properties of the network and the dynamics of evolution. In particular, we develop a mathematical theory that accurately predicts the epidemic threshold and the expected epidemic size as functions of the characteristics of the spreading process, the evolutionary dynamics of the pathogen, and the structure of the underlying contact network. In addition to the mathematical theory, we perform extensive simulations on random and real-world contact networks to verify our theory and reveal the significant shortcomings of the classical mathematical models that do not capture evolution. Our results reveal that the classical, single-type bond-percolation models may accurately predict the threshold and final size of epidemics, but their predictions on the probability of emergence are inaccurate on both random and real-world networks. This inaccuracy sheds the light on a fundamental disconnect between the classical bond-percolation models and real-life spreading processes that entail evolution. Finally, we consider the case when co-infection is possible and show that co-infection could lead the order of phase transition to change from second-order to first-order.Comment: Submitte