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

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. History: Bianca Maria Colosimo served as the senior editor. Funding: C. Zhang is partially supported by the NSFC [Grants 71932006 and 72271138], the BNSF [Grant 9222014], and the ASFC [Grant 2020Z063058001]. H. Yan is partially supported by NIH [R21 AI157618] and NSF [CMMI 2316654]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijds.2022.00011 . Data Ethics & Reproducibility Note: No data ethics considerations are foreseen related to this paper. The code capsule is available on Code Ocean at https://codeocean.com/capsule/8794940/tree/v1 and in the e-Companion to this article (available at https://doi.org/10.1287/ijds.2022.00011 ).