Large-scale and Deep Spatiotemporal Point-Process Models

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

Multivariate Spatiotemporal Hawkes Processes and Network Reconstruction

There is often latent network structure in spatial and temporal data and the tools of network analysis can yield fascinating insights into such data. In this paper, we develop a nonparametric method for network reconstruction from spatiotemporal data sets using multivariate Hawkes processes. In contrast to prior work on network reconstruction with point-process models, which has often focused on exclusively temporal information, our approach uses both temporal and spatial information and does not assume a specific parametric form of network dynamics. This leads to an effective way of recovering an underlying network. We illustrate our approach using both synthetic networks and networks constructed from real-world data sets (a location-based social media network, a narrative of crime events, and violent gang crimes). Our results demonstrate that, in comparison to using only temporal data, our spatiotemporal approach yields improved network reconstruction, providing a basis for meaningful subsequent analysis --- such as community structure and motif analysis --- of the reconstructed networks

SOS-EW: System for Overdose Spike Early Warning Using Drug Mover’s Distance-Based Hawkes Processes

Opioid addictions and overdoses have increased across the U.S. and internationally over the past decade. In urban environments, overdoses cluster in space and time, with 50% of overdoses occurring in less than 5% of the city and dozens of calls for emergency medical services being made within a 48-hour period. In this work, we introduce a system for early detection of opioid overdose clusters based upon the toxicology report of an initial event. We first use drug SMILES, one hot encoded molecular substructures, to generate a bag of drug vectors corresponding to each overdose (overdoses are often characterized by multiple drugs taken at the same time). We then use spectral clustering to generate overdose categories and estimate multivariate Hawkes processes for the space-time intensity of overdoses following an initial event. As the productivity parameter of the process depends on the overdose category, this allows us to estimate the magnitude of an overdose spike based on the substances present (e.g. fentanyl leads to more subsequent overdoses compared to Oxycontin). We validate the model using opioid overdose deaths in Indianapolis and show that the model outperforms several recently introduced Hawkes-Topic models based on Dirichlet processes. Our system could be used in combination with drug test strips to alert drug using populations of risky batches on the market or to more efficiently allocate naloxone to users and health/social workers

Machine learning for cardiac ultrasound time series data

We consider the problem of identifying frames in a cardiac ultrasound video associated with left ventricular chamber end-systolic (ES, contraction) and end-diastolic (ED, expansion) phases of the cardiac cycle. Our procedure involves a simple application of non-negative matrix factorization (NMF) to a series of frames of a video from a single patient. Rank-2 NMF is performed to compute two end-members. The end members are shown to be close representations of the actual heart morphology at the end of each phase of the heart function. Moreover, the entire time series can be represented as a linear combination of these two end-member states thus providing a very low dimensional representation of the time dynamics of the heart. Unlike previous work, our methods do not require any electrocardiogram (ECG) information in order to select the end-diastolic frame. Results are presented for a data set of 99 patients including both healthy and diseased examples.UCLA through the Physical Sciences Division; Entrepreneurship and Innovation Fund; Department of Mathematics; NSF [DMS-1045536, DMS-1417674]; ONR [N00014-16-1-2119]; Cross-disciplinary Scholars in Science and Technology (CSST) program at UCLACPCI-S(ISTP)1013

Large-scale and Deep Spatiotemporal Point-Process Models

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

Multivariate Spatiotemporal Hawkes Processes and Network Reconstruction

There is often latent network structure in spatial and temporal data and the tools of network analysis can yield fascinating insights into such data. In this paper, we develop a nonparametric method for network reconstruction from spatiotemporal data sets using multivariate Hawkes processes. In contrast to prior work on network reconstruction with point-process models, which has often focused on exclusively temporal information, our approach uses both temporal and spatial information and does not assume a specific parametric form of network dynamics. This leads to an effective way of recovering an underlying network. We illustrate our approach using both synthetic networks and networks constructed from real-world data sets (a location-based social media network, a narrative of crime events, and violent gang crimes). Our results demonstrate that, in comparison to using only temporal data, our spatiotemporal approach yields improved network reconstruction, providing a basis for meaningful subsequent analysis --- such as community structure and motif analysis --- of the reconstructed networks