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  1. Abstract

    Most COVID-19 studies commonly report figures of the overall infection at a state- or county-level. This aggregation tends to miss out on fine details of virus propagation. In this paper, we analyze a high-resolution COVID-19 dataset in Cali, Colombia, that records the precise time and location of every confirmed case. We develop a non-stationary spatio-temporal point process equipped with a neural network-based kernel to capture the heterogeneous correlations among COVID-19 cases. The kernel is carefully crafted to enhance expressiveness while maintaining model interpretability. We also incorporate some exogenous influences imposed by city landmarks. Our approach outperforms the state-of-the-art in forecasting new COVID-19 cases with the capability to offer vital insights into the spatio-temporal interaction between individuals concerning the disease spread in a metropolis.

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  6. We consider the sequential anomaly detection problem in the one-class setting when only the anomalous sequences are available and propose an adversarial sequential detector by solving a minimax problem to find an optimal detector against the worst-case sequences from a generator. The generator captures the dependence in sequential events using the marked point process model. The detector sequentially evaluates the likelihood of a test sequence and compares it with a time-varying threshold, also learned from data through the minimax problem. We demonstrate our proposed method’s good performance using numerical experiments on simulations and proprietary large-scale credit card fraud data sets. The proposed method can generally apply to detecting anomalous sequences. History: W. Nick Street served as the senior editor for this article. Funding: This work is partially supported by the National Science Foundation [Grants CAREER CCF-1650913, DMS-1938106, and DMS-1830210] and grant support from Macy’s Technology. Data Ethics & Reproducibility Note: The code capsule is available on Code Ocean at and in the e-Companion to this article (available at ). 
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    Free, publicly-accessible full text available April 1, 2024