Modeling and detection using high-dimensional time series data
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Gong, Tingnan
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Abstract
Change-point detection and point process modeling play a vital role in time series analysis, particularly when the data are high-dimensional, correlated, or observed under time uncertainty. For high-dimensional data with complex spatio-temporal correlations and minimal distributional assumptions, real-time detection of distributional shifts requires carefully designed procedures that address multiple statistical and computational challenges. For event data with time uncertainty, to the best of our knowledge, no existing work has established a point process model that explicitly incorporates time uncertainty. This thesis develops new methods for online change-point detection in complex high-dimensional data and for point process modeling under time uncertainty. We propose a distribution-free CUSUM procedure for low-rank image data, which avoids parametric noise assumptions and demonstrates reliable detection performance in manufacturing applications. We also develop a neural network-based detection procedure via a binary classification proxy to flexibly adapt to various types of distributional shifts. Additionally, a higher-criticism-based approach is developed for detecting sparse and weak changes in high-dimensional signals, achieving asymptotically optimal detection delay under rare moderate departure regimes with theoretical guarantees. Finally, a novel framework is introduced for modeling point processes with time uncertainty; through a carefully designed training scheme and kernel-based parameterization, the model predicts event occurrence probabilities and recovers dynamic causal structures in both simulations and real-world datasets such as Sepsis medical records and urban burglary incidents.
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2025-05-08
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Dissertation