Active hypothesis testing on a tree: Anomaly detection under hierarchical observations

Wang, Chao; Cohen, Kobi; Zhao, Qing

doi:10.1109/isit.2017.8006677

Cited by 14 publications

(9 citation statements)

References 28 publications

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“…There are various mechanisms to probe these processes and the objective is to reliably detect the anomaly as quickly as possible. Some recent works in anomaly detection include [14]- [18]. All these works are in the sequential setting.…”

Section: ) Fixed-horizon Hypothesis Testingmentioning

confidence: 99%

Fixed-horizon Active Hypothesis Testing

Kartik¹,

Nayyar²,

Mitra³

2019

Preprint

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Two active hypothesis testing problems are formulated. In these problems, the agent can perform a fixed number of experiments and then decide on one of the hypotheses. The agent is also allowed to declare its experiments inconclusive if needed. The first problem is an asymmetric formulation in which the the objective is to minimize the probability of incorrectly declaring a particular hypothesis to be true while ensuring that the probability of correctly declaring that hypothesis is moderately high. This formulation can be seen as a generalization of the formulation in the classical Chernoff-Stein lemma to an active setting. The second problem is a symmetric formulation in which the objective is to minimize the probability of making an incorrect inference (misclassification probability) while ensuring that the true hypothesis is declared conclusively with moderately high probability. For these problems, lower and upper bounds on the optimal misclassification probabilities are derived and these bounds are shown to be asymptotically tight. Classical approaches for experiment selection suggest use of randomized and, in some cases, open-loop strategies. As opposed to these classical approaches, fully deterministic and adaptive experiment selection strategies are provided. It is shown that these strategies are asymptotically optimal and further, using numerical experiments, it is demonstrated that these novel experiment selection strategies (coupled with appropriate inference strategies) have a significantly better performance in the non-asymptotic regime.

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Section: ) Fixed-horizon Hypothesis Testingmentioning

confidence: 99%

Fixed-horizon Active Hypothesis Testing

Kartik¹,

Nayyar²,

Mitra³

2019

Preprint

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“…Establishing the optimal nested test plan under these group testing models are interesting future directions. Since SQGT and TGT can be considered as noisy group testing with specific noise models, a recent result in [56] on a tree-structured adaptive strategy for general noisy group testing may be applicable, even though the special noise models in SQGT and TGT may be exploited for better performance. Together with (8), we arrive at…”

Section: Discussionmentioning

confidence: 99%

Optimal Nested Test Plan for Combinatorial Quantitative Group Testing

Wang

Zhao

Chuah

2018

IEEE Trans. Signal Process.

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We consider the quantitative group testing problem where the objective is to identify defective items in a given population based on results of tests performed on subsets of the population. Under the quantitative group testing model, the result of each test reveals the number of defective items in the tested group. The minimum number of tests achievable by nested test plans was established by Aigner and Schughart in 1985 within a minimax framework. The optimal nested test plan offering this performance, however, was not obtained. In this work, we establish the optimal nested test plan in closed form. This optimal nested test plan is also order optimal among all test plans as the population size approaches infinity. Using heavy-hitter detection as a case study, we show via simulation examples orders of magnitude improvement of the group testing approach over two prevailing sampling-based approaches in detection accuracy and counter consumption. Other applications include anomaly detection and wideband spectrum sensing in cognitive radio systems.

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“…Some recent works in anomaly detection include [12]- [16]. All these works are in the sequential setting and focus on asymptotic optimality.…”

Section: A Related Workmentioning

confidence: 99%

Testing for Anomalies: Active Strategies and Non-asymptotic Analysis

Kartik¹,

Nayyar²,

Mitra³

2020

Preprint

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The problem of verifying whether a multicomponent system has anomalies or not is addressed. Each component can be probed over time in a data-driven manner to obtain noisy observations that indicate whether the selected component is anomalous or not. The aim is to minimize the probability of incorrectly declaring the system to be free of anomalies while ensuring that the probability of correctly declaring it to be safe is sufficiently large. This problem is modeled as an active hypothesis testing problem in the Neyman-Pearson setting. Componentselection and inference strategies are designed and analyzed in the non-asymptotic regime. For a specific class of homogeneous problems, stronger (with respect to prior work) non-asymptotic converse and achievability bounds are provided.

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Active hypothesis testing on a tree: Anomaly detection under hierarchical observations

Cited by 14 publications

References 28 publications

Fixed-horizon Active Hypothesis Testing

Fixed-horizon Active Hypothesis Testing

Optimal Nested Test Plan for Combinatorial Quantitative Group Testing

Testing for Anomalies: Active Strategies and Non-asymptotic Analysis

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