Thompson Sampling-Based Partially Observable Online Change Detection for Exponential Families

Jie Guo (), Hao Yan () and Chen Zhang ()
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Jie Guo: Department of Industrial Engineering, Tsinghua University, Beijing 100084, China
Hao Yan: School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, Tempe, Arizona 85287
Chen Zhang: Department of Industrial Engineering, Tsinghua University, Beijing 100084, China

INFORMS Joural on Data Science, 2024, vol. 3, issue 2, 145-161

Abstract: This paper proposes a holistic sequential change detection framework for partially observable high-dimensional data streams with exponential-family distributions. The framework first proposes a general composite decomposition for exponential-family distributed data by projecting its natural parameter onto normal bases and abnormal bases, which enables efficient inference for sparse changes. Then, the inference results are used for detection scheme construction, and different types of test statistics can be compacted in our framework. Last, by further designing the test statistic as the reward function in the combinatorial multi-armed bandit problem, a Thompson sampling-based sensor allocation strategy is constructed to select the most anomalous variables. Theoretical properties of the detection framework are discussed. Finally, examples of Gaussian, Poisson, and binomial distributed data streams are given in numerical studies and case studies to evaluate the performance of our proposed method.

Keywords: sequential sparse change detection; partially observable data; Bayesian framework; combinatorial multi-armed bandit; Thompson sampling; exponential family (search for similar items in EconPapers)
Date: 2024
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