In this work, we study a stopping time game problem in sequential hypothesis testing, where both of the two players perform hypothesistesting with distinct hypotheses. The payoff of the players depends on the order o...
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ISBN:
(纸本)9781728140841
In this work, we study a stopping time game problem in sequential hypothesis testing, where both of the two players perform hypothesistesting with distinct hypotheses. The payoff of the players depends on the order of stopping times. Therefore, apart from designing the decision function concerning the hypotheses, the players also determine the optimal stopping timings. We investigate the cases where the time horizon is finite or infinite and provide sufficient conditions of finding the equilibrium point. Moreover, we fully characterize the structural properties of the equilibrium strategies.
In this paper, we propose two online algorithms to detect 802.11 traffic from packet-header data collected passively at a monitoring point. These algorithms have a number of applications in real-time wireless LAN mana...
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In this paper, we propose two online algorithms to detect 802.11 traffic from packet-header data collected passively at a monitoring point. These algorithms have a number of applications in real-time wireless LAN management, for instance, in detecting unauthorized access points and detecting/predicting performance degradations. Both algorithms use sequentialhypothesis tests and exploit fundamental properties of the 802.11 CSMA/CA MAC protocol and the half-duplex nature of wireless channels. They differ in that one requires training sets, while the other does not. We have built a system for online wireless traffic detection using these algorithms and deployed it at a university gateway router. Extensive experiments have demonstrated the effectiveness of our approach: the algorithm that requires training provides rapid detection and is extremely accurate (the detection is mostly within 10 seconds, with very low false-positive and false-negative ratios), the algorithm that does not require training detects 60 percent to 76 percent of the wireless hosts without any false positives, and both algorithms are lightweight, with computation and storage overhead well within the capability of commodity equipment.
Under some mild Markov assumptions it is shown that the problem of designing optimal sequential tests for two simple hypotheses can be formulated as a linear program. This result is derived by investigating the Lagran...
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Under some mild Markov assumptions it is shown that the problem of designing optimal sequential tests for two simple hypotheses can be formulated as a linear program. This result is derived by investigating the Lagrangian dual of the sequentialtesting problem, which is an unconstrained optimal stopping problem depending on two unknown Lagrangian multipliers. It is shown that the derivative of the optimal cost function, with respect to these multipliers, coincides with the error probabilities of the corresponding sequential test. This property is used to formulate an optimization problem that is jointly linear in the cost function and the Lagrangian multipliers and can be solved for both with off-the-shelf algorithms. To illustrate the procedure, optimal sequential tests for Gaussian random sequences with different dependency structures are derived, including the Gaussian AR(1) process.
This paper describes a method for robust real-time pattern matching. We first introduce a family of image distance measures, the Image Hamming Distance Family. Members of this family are robust to occlusion, small geo...
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This paper describes a method for robust real-time pattern matching. We first introduce a family of image distance measures, the Image Hamming Distance Family. Members of this family are robust to occlusion, small geometrical transforms, light changes, and nonrigid deformations. We then present a novel Bayesian framework for sequential hypothesis testing on finite populations. Based on this framework, we design an optimal rejection/acceptance sampling algorithm. This algorithm quickly determines whether two images are similar with respect to a member of the Image Hamming Distance Family. We also present a fast framework that designs a near-optimal sampling algorithm. Extensive experimental results show that the sequential sampling algorithm's performance is excellent. Implemented on a Pentium IV 3 GHz processor, the detection of a pattern with 2,197 pixels in 640 x 480 pixel frames, where in each frame the pattern rotated and was highly occluded, proceeds at only 0.022 seconds per frame.
We consider the problem of sensor selection for time-optimal detection of a hypothesis. We consider a group of sensors transmitting their observations to a fusion center. The fusion center considers the output of only...
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We consider the problem of sensor selection for time-optimal detection of a hypothesis. We consider a group of sensors transmitting their observations to a fusion center. The fusion center considers the output of only one randomly chosen sensor at the time, and performs a sequentialhypothesis test. We study a sequential multiple hypothesis test with randomized sensor selection strategy. We incorporate the random processing times of the sensors to determine the asymptotic performance characteristics of this test. For three distinct performance metrics, we show that, for a generic set of sensors and binary hypothesis, the time-optimal policy requires the fusion center to consider at most two sensors. We also show that for the case of multiple hypothesis, the time-optimal policy needs at most as many sensors to be observed as the number of underlying hypotheses.
An asymptotically optimum test for the problem of decentralized sequential hypothesis testing is presented. The induced communication between sensors and fusion center is asynchronous and limited to 1-bit data. When t...
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An asymptotically optimum test for the problem of decentralized sequential hypothesis testing is presented. The induced communication between sensors and fusion center is asynchronous and limited to 1-bit data. When the sensors observe continuously stochastic processes with continuous paths, the proposed test is order-2 asymptotically optimal, in the sense that its inflicted performance loss is bounded. When the sensors take discrete time observations, the proposed test achieves order-1 asymptotic optimality, i.e., the ratio of its performance over the optimal performance tends to 1. Moreover, we show theoretically and corroborate with simulations that the performance of the suggested test in discrete time can be significantly improved when the sensors sample their underlying continuous time processes more frequently, a property which is not enjoyed by other centralized or decentralized tests in the literature.
An interesting question is whether an information theoretic interpretation can be given of optimal algorithms in sequential hypothesis testing. We prove that for the binary sequen-tial probability ratio test of a cont...
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An interesting question is whether an information theoretic interpretation can be given of optimal algorithms in sequential hypothesis testing. We prove that for the binary sequen-tial probability ratio test of a continuous observation process, the mutual information between the observation process up to the decision time and the actual hypothesis conditioned on the decision variable is equal to zero. This result can be interpreted as an optimal usage of the information on the hypothesis available in the observations by the sequential probability ratio test. As a consequence, the mutual information between the random decision time of the sequential probability ratio test and the actual hypothesis conditioned on the decision variable is also equal to zero.
It is well known that duty-cycling control by dynamically adjusting the polling interval according to the traffic loads can effectively achieve power saving in wireless sensor networks. Thus, there has been a signific...
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It is well known that duty-cycling control by dynamically adjusting the polling interval according to the traffic loads can effectively achieve power saving in wireless sensor networks. Thus, there has been a significant research effort in developing polling interval adaptation schemes. Especially, Dynamic Low Power Listening (DLPL) scheme is one of the most widely adopted open-looping polling interval adaptation techniques in wireless sensor networks. In DLPL scheme, if consecutive idle (busy) samplings reach a given fixed threshold, the polling interval is increased (decreased). However, due to the trial-and-error based approach, it may significantly deteriorate the system performance depending on given threshold parameters. In this paper, we propose a novel DLPL scheme, called SDL (sequential hypothesis testing based Dynamic LPL), which employs sequential hypothesis testing to decide whether to change the polling interval conforming to various traffic conditions. Simulation results show that SDL achieves substantial power saving over state-of-the-art DLPL schemes.
We consider the classical sequential binary hypothesistesting problem in which there are two hypotheses governed respectively by distributions P-0 and P-1 and we would like to decide which hypothesis is true using a ...
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We consider the classical sequential binary hypothesistesting problem in which there are two hypotheses governed respectively by distributions P-0 and P-1 and we would like to decide which hypothesis is true using a sequential test. It is known from the work of Wald and Wolfowitz that as the expectation of the length of the test grows, the optimal type-I and type-II error exponents approach the relative entropies D(P-1 parallel to P-0) and D(P-0 parallel to P-1). We refine this result by considering the optimal backoff-or second-order asymptotics-from the corner point of the achievable exponent region (D(P-1 parallel to P-0), D(P-0 parallel to P-1)) under two different constraints on the length of the test (or the sample size). First, we consider a probabilistic constraint in which the probability that the length of test exceeds a prescribed integer n is less than a certain threshold 0 < epsilon < 1. Second, the expectation of the sample size is bounded by n. In both cases, and under mild conditions, the second-order asymptotics is characterized exactly. Numerical examples are provided to illustrate our results.
This paper considers a novel formulation of inverse reinforcement learning with behavioral economics constraints to address inverse sequential hypothesis testing (SHT) in Bayesian agents. The aim is to estimate the de...
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ISBN:
(纸本)9780578647098
This paper considers a novel formulation of inverse reinforcement learning with behavioral economics constraints to address inverse sequential hypothesis testing (SHT) in Bayesian agents. The aim is to estimate the detection costs by observing the actions of the sequentialhypothesis detector. Our methodology involves Bayesian revealed preferences from microeconomics and rational inattention from behavioral economics. First, we show that Bayesian agents optimally performing SHT are rationally inattentive utility maximizers. Using established results in Bayesian revealed preferences, we outline a feasibility test for a data analyst observing the Bayesian agents to estimate their detection costs. Numerical examples illustrate the performance of the inverse sequential hypothesis testing algorithm.
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