1,705 research outputs found
Asymptotically Optimal Anomaly Detection via Sequential Testing
Sequential detection of independent anomalous processes among K processes is
considered. At each time, only M processes can be observed, and the
observations from each chosen process follow two different distributions,
depending on whether the process is normal or abnormal. Each anomalous process
incurs a cost per unit time until its anomaly is identified and fixed.
Switching across processes and state declarations are allowed at all times,
while decisions are based on all past observations and actions. The objective
is a sequential search strategy that minimizes the total expected cost incurred
by all the processes during the detection process under reliability
constraints. Low-complexity algorithms are established to achieve
asymptotically optimal performance as the error constraints approach zero.
Simulation results demonstrate strong performance in the finite regime.Comment: 28 pages, 5 figures, part of this work will be presented at the 52nd
Annual Allerton Conference on Communication, Control, and Computing, 201
Active Search with a Cost for Switching Actions
Active Sequential Hypothesis Testing (ASHT) is an extension of the classical
sequential hypothesis testing problem with controls. Chernoff (Ann. Math.
Statist., 1959) proposed a policy called Procedure A and showed its asymptotic
optimality as the cost of sampling was driven to zero. In this paper we study a
further extension where we introduce costs for switching of actions. We show
that a modification of Chernoff's Procedure A, one that we call Sluggish
Procedure A, is asymptotically optimal even with switching costs. The growth
rate of the total cost, as the probability of false detection is driven to
zero, and as a switching parameter of the Sluggish Procedure A is driven down
to zero, is the same as that without switching costs.Comment: 8 pages. Presented at 2015 Information Theory and Applications
Worksho
Active Anomaly Detection in Heterogeneous Processes
An active inference problem of detecting anomalies among heterogeneous
processes is considered. At each time, a subset of processes can be probed. The
objective is to design a sequential probing strategy that dynamically
determines which processes to observe at each time and when to terminate the
search so that the expected detection time is minimized under a constraint on
the probability of misclassifying any process. This problem falls into the
general setting of sequential design of experiments pioneered by Chernoff in
1959, in which a randomized strategy, referred to as the Chernoff test, was
proposed and shown to be asymptotically optimal as the error probability
approaches zero. For the problem considered in this paper, a low-complexity
deterministic test is shown to enjoy the same asymptotic optimality while
offering significantly better performance in the finite regime and faster
convergence to the optimal rate function, especially when the number of
processes is large. The computational complexity of the proposed test is also
of a significantly lower order.Comment: This work has been accepted for publication on IEEE Transactions on
Information Theor
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