Extremal properties of likelihood-ratio quantizers

Tsitsiklis, John N.

doi:10.1109/26.223779

Cited by 107 publications

(119 citation statements)

References 20 publications

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“…The network aims to minimize the probability of error or some other cost function at the fusion center, by choosing optimal transmission functions and fusion rules. Various properties and variants of the decentralized detection problem in a parallel configuration have been extensively studied over the last twenty-five years; examples include the following: [4][5][6][7][8] study the properties of optimal fusion rules and quantizers at sensor nodes; [9] shows the existence of optimal strategies, and proves that likelihood ratio quantizers are optimal for a large class of problems including the decentralized detection problem; and [10][11][12][13][14] consider constrained decentralized detection. The reader is referred to [15,16] for a survey of the work done in this area.…”

Section: Introductionmentioning

confidence: 99%

Error Exponents for Decentralized Detection in Tree Networks

Tay

Tsitsiklis

2008

Networked Sensing Information and Control

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Summary. We consider the problem of decentralized detection in a sensor network consisting of nodes arranged as a tree of bounded height. We characterize the optimal error exponent under a Neyman-Pearson formulation, and show that the Type II error probability decays exponentially with the number of nodes. Surprisingly, the optimal error exponent is often the same as that corresponding to a parallel configuration. We provide sufficient, as well as necessary, conditions for this to happen. We also consider the impact of failure-prone sensors or unreliable communications between sensors on the detection performance. Simple strategies that nearly achieve the asymptotically optimal performance in these cases are also developed.

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Section: Introductionmentioning

confidence: 99%

Error Exponents for Decentralized Detection in Tree Networks

Tay

Tsitsiklis

2008

Networked Sensing Information and Control

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“…, N : Q a = X N j=1 Q j . As previously mentioned, it has been proved in [9] that Q j is a compact set, and thus any cost function that is a continuous function on Q j will attain a minimum. In a parallel configuration with multiple sensors and a fusion center, if the sensor observations are independent given each hypothesis, it has also been shown that there exists an optimal solution over the set Q a [9].…”

Section: A Backgroundmentioning

confidence: 93%

“…, D − 1}, each sensor can be considered as a quantizer. As mentioned in the Introduction, [9] characterizes these quantizers based on the set of marginal distributions of the messages given each hypothesis. Following [9], let…”

Section: A Backgroundmentioning

confidence: 99%

“…For a single sensor, it has been proved in [9] that the set of conditional distributions, Q, is a compact set, and thus any cost function that is a continuous function on Q will attain a minimum, which corresponds to an optimal quantizer. In a parallel configuration with multiple sensors and a fusion center, if the sensor observations are independent given each hypothesis, it has also been shown in [9] that there exists an optimal solution over the Cartesian product of the sets of conditional marginal probabilities {P i (d)}, i ∈ {0, 1, .…”

Section: Introductionmentioning

confidence: 99%

“…In a parallel configuration with multiple sensors and a fusion center, if the sensor observations are independent given each hypothesis, it has also been shown in [9] that there exists an optimal solution over the Cartesian product of the sets of conditional marginal probabilities {P i (d)}, i ∈ {0, 1, . .…”

Section: Introductionmentioning

confidence: 99%

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Distributed hypothesis testing with a fusion center: The conditionally dependent case

Nguyen

Alpcan

Başar

2008

2008 47th IEEE Conference on Decision and Control

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Abstract-The paper deals with decentralized Bayesian detection with M hypotheses, and N sensors making conditionally correlated measurements regarding these hypotheses. Each sensor sends to a fusion center an integer from {0, 1, .., D − 1}, and the fusion center makes a decision on the actual hypothesis based on the messages it receives from the sensors so as to minimize the average probability of error. Such conditionally dependent scenarios arise in several applications of decentralized detection such as sensor networks and network security. Conditional dependence leads to a non-standard distributed decision problem where threshold based policies (on likelihood ratios) are no longer optimal, which results in a challenging distributed optimization/decision making problem. We show that, in this case, the minimum average probability of error cannot be expressed as a function of the marginal distributions of the sensor messages. Instead, we characterize this probability based on the joint distributions of these messages. We also provide some numerical results for the case where the sensors' measurements follow bivariate normal distributions.

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A Decentralized Bayesian Attack Detection Algorithm for Network Security

Nguyen

Alpcan

Basar

Proceedings of the Ifip Tc 11 23rd International Information Security Conference

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Decentralized detection has been an active area of research since the late 1970s. Its earlier application area has been distributed radar systems, and more recently it has found applications in sensor networks and intrusion detection. The most popular decentralized detection network structure is the parallel configuration, where a number of sensors are directly connected to a fusion center. The sensors receive measurements related to an event and then send summaries of their observations to the fusion center. Previous work has focused on separate optimization of the quantization rules at the sensors and the fusion rule at the fusion center or on asymptotic results when the number of sensors is very large and the observations are conditionally independent and identically distributed given each hypothesis.In this work, we examine the application of decentralized detection to intrusion detection with again the parallel configuration, but with joint optimization. Particularly, using the Bayesian approach, we seek a joint optimization of the quantization rules at the sensors and the fusion rule at the fusion center. The observations of the sensors are not assumed to be conditionally independent nor identically distributed. We consider the discrete case where the distributions of the observations are given as probability mass functions. We propose a search algorithm for the optimal solution. Simulations carried out using the KDD'99 intrusion detection dataset show that the algorithm performs well.

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Extremal properties of likelihood-ratio quantizers

Cited by 107 publications

References 20 publications

Error Exponents for Decentralized Detection in Tree Networks

Error Exponents for Decentralized Detection in Tree Networks

Distributed hypothesis testing with a fusion center: The conditionally dependent case

A Decentralized Bayesian Attack Detection Algorithm for Network Security

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