@inproceedings{b241f22bcd0e4a0db20d36fd35c59d4d,

title = "Active hypothesis testing on a tree: Anomaly detection under hierarchical observations",

abstract = "The problem of detecting a few anomalous processes among a large number of M processes is considered. At each time, aggregated observations can be taken from a chosen subset of processes, where the chosen subset conforms to a given binary tree structure. The random observations are i.i.d. over time with a general distribution that may depend on the size of the chosen subset and the number of anomalous processes in the subset. The objective is a sequential search strategy that minimizes the sample complexity (i.e., the expected number of observations which represents detection delay) subject to a reliability constraint. A sequential test that results in a biased random walk on the tree is developed and is shown to be asymptotically optimal in terms of detection accuracy. Furthermore, it achieves the optimal logarithmic-order sample complexity in M provided that the Kullback-Liebler divergence between aggregated observations in the presence and the absence of anomalous processes are bounded away from zero at all levels of the tree structure as M approaches infinity. Sufficient conditions on the decaying rate of the aggregated observations to pure noise under which a sublinear scaling in M is preserved are also identified for the Bernoulli case.",

keywords = "Active hypothesis testing, Anomaly detection, Noisy group testing, Random walk, Sequential design of experiments",

author = "Chao Wang and Kobi Cohen and Qing Zhao",

note = "Funding Information: The work of C. Wang and Q. Zhao was supported by the National Science Foundation under Grant CCF-1320065. The work of K. Cohen was partially supported by the Cyber Security Research Center at Ben-Gurion University of the Negev. Publisher Copyright: {\textcopyright} 2017 IEEE.; 2017 IEEE International Symposium on Information Theory, ISIT 2017 ; Conference date: 25-06-2017 Through 30-06-2017",

year = "2017",

month = aug,

day = "9",

doi = "10.1109/ISIT.2017.8006677",

language = "English",

series = "IEEE International Symposium on Information Theory - Proceedings",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "993--997",

booktitle = "2017 IEEE International Symposium on Information Theory, ISIT 2017",

address = "United States",

}