Neyman-Pearson（NP） criterion is one of the most important ways in hypothesis testing. It is also a criterion for classification. This paper addresses the problem of bounding the estimation error of NP classification...Neyman-Pearson（NP） criterion is one of the most important ways in hypothesis testing. It is also a criterion for classification. This paper addresses the problem of bounding the estimation error of NP classification, in terms of Rademacher averages. We investigate the behavior of the global and local Rademacher averages, and present new NP classification error bounds which are based on the localized averages, and indicate how the estimation error can be estimated without a priori knowledge of the class at hand.展开更多
Neyman-Pearson classification has been studied in several articles before. But they all proceeded in the classes of indicator functions with indicator function as the loss function, which make the calculation to be di...Neyman-Pearson classification has been studied in several articles before. But they all proceeded in the classes of indicator functions with indicator function as the loss function, which make the calculation to be difficult. This paper investigates Neyman- Pearson classification with convex loss function in the arbitrary class of real measurable functions. A general condition is given under which Neyman-Pearson classification with convex loss function has the same classifier as that with indicator loss function. We give analysis to NP-ERM with convex loss function and prove it＇s performance guarantees. An example of complexity penalty pair about convex loss function risk in terms of Rademacher averages is studied, which produces a tight PAC bound of the NP-ERM with convex loss function.展开更多
The problem of distributed detection fusion using multiple sensors for remote underwater target detection is studied. Considering that multiple access channel （MAC） schemes are able to offer high efficiency in bandw...The problem of distributed detection fusion using multiple sensors for remote underwater target detection is studied. Considering that multiple access channel （MAC） schemes are able to offer high efficiency in bandwidth usage and consume less energy than the parallel access channel （PAC）, the MAC scheme is introduced into the underwater target detection field. The model of underwater distributed detection fusion based on MAC schemes is established. A new method for detection fusion of MAC based on deflection coefficient maximization （DCM） and Neyman-Pearson （NP） rule is proposed. Under the power constraint of local sensors, this paper uses the DCM theory to derive the optimal weight coefficients and offsets. The closed-form expressions of detection probability and false alarm probability for fusion systems are obtained. The optimal detection performance of fusion systems is analyzed and deeply researched. Both the theory analysis and simulation experiments indicate that the proposed method could improve the detection performance and decrease the error probability effectively under power constraints of local sensors and low signal to noise ratio.展开更多
The stability of testing hypotheses is discussed.Differing from the usual tests measured by Neyman-Pearson lemma,the regret and correction of the tests are considered.After the decision is made based on the observatio...The stability of testing hypotheses is discussed.Differing from the usual tests measured by Neyman-Pearson lemma,the regret and correction of the tests are considered.After the decision is made based on the observations X1,X2,...,Xn,one more piece of datum Xn+1 is picked and the test is done again in the same way but based on X1,X2,...,Xn,Xn+1.There are three situations;(i) The previous decision is right but the new decision is wrong; (ii) the previous decision is wrong but the new decision is right; (iii) both of them are right or both of them are wrong.Of course,it is desired that the probability of the occurrence of (i) is as small as possible and the probability of the occurrence of (ii) is as large as possible.Since the sample size is sometimes not chosen very precisely after the type Ⅰ error and the type Ⅱ error are determined in practice,it seems more urgent to consider the above problem.Some optimal plans are also given.展开更多
The performance of a distributed Neyman-Pearson detection system is considered with the decision rules of the sensors given and the decisions from different sensors being mutually independent conditioned on both hypot...The performance of a distributed Neyman-Pearson detection system is considered with the decision rules of the sensors given and the decisions from different sensors being mutually independent conditioned on both hypothese. To achieve the better performance at the fusion center for a general detection system of n 〉 3 sensor configuration, the necessary and sufficient conditions are derived by comparing the probability of detec- tion at the fusion center with that of each of the sensors, with the constraint that the probability of false alarm at the fusion center is equal to that of the sensor. The conditions are related with the performances of the sensors and using the results we can predict the performance at the fusion center of a distributed detection system and can choose appropriate sensors to construct efficient distributed detection systems.展开更多
For the two side truncated distribution family: dPθ(x) = f(x;θ1θ2)I(θ≤ x≤θ2)dx, where θ=(θ1,θ2),θ < θ2,chen & Fu studied one side asymptotic efficiency of the estimator for parameter hation g(θ) =...For the two side truncated distribution family: dPθ(x) = f(x;θ1θ2)I(θ≤ x≤θ2)dx, where θ=(θ1,θ2),θ < θ2,chen & Fu studied one side asymptotic efficiency of the estimator for parameter hation g(θ) = c1θ1 + C2θ2, they pointed out that when c1c2≥0, there exist one side asymptotic efficient estimators for g(θ); when c1c2 < 0, the estimator they proposed is not asymptotically efficient. Then they put forward a question: Is there any other asymptotically efficient estimator for g(θ) when c1c2 <0? In this paper, we study this problem, we prove that when the distribution under consideration is uniform distribution with location and scale parameters, there does not exist one side asymptotically efficient estimators for the scale parameter.展开更多
In order to solve the distributed detection fusion problem of underwater target detection, when the signal to noise ratio (SNR) of the acoustic channel is low, a new strategy for united detection fusion and communicat...In order to solve the distributed detection fusion problem of underwater target detection, when the signal to noise ratio (SNR) of the acoustic channel is low, a new strategy for united detection fusion and communication using multiple sensors was proposed. The performance of detection fusion was studied and compared based on the Neyman-Pearson principle when the binary phase shift keying (BPSK) and on-off keying (OOK) modes were used by the local sensors. The comparative simulation and analysis between the optimal likelihood ratio test and the proposed strategy was completed, and both the theoretical analysis and simulation indicate that using the proposed new strategy could improve the detection performance effectively. In theory, the proposed strategy of united detection fusion and communication is of great significance to the establishment of an underwater target detection system.展开更多
基金Research supported in part by NSF of China under Grant Nos. 10801004, 10871015supported in part by Startup Grant for Doctoral Research of Beijing University of Technology
文摘Neyman-Pearson（NP） criterion is one of the most important ways in hypothesis testing. It is also a criterion for classification. This paper addresses the problem of bounding the estimation error of NP classification, in terms of Rademacher averages. We investigate the behavior of the global and local Rademacher averages, and present new NP classification error bounds which are based on the localized averages, and indicate how the estimation error can be estimated without a priori knowledge of the class at hand.
基金This is a Plenary Report on the International Symposium on Approximation Theory and Remote SensingApplications held in Kunming, China in April 2006Supported in part by NSF of China under grants 10571010 , 10171007 and Startup Grant for Doctoral Researchof Beijing University of Technology
文摘Neyman-Pearson classification has been studied in several articles before. But they all proceeded in the classes of indicator functions with indicator function as the loss function, which make the calculation to be difficult. This paper investigates Neyman- Pearson classification with convex loss function in the arbitrary class of real measurable functions. A general condition is given under which Neyman-Pearson classification with convex loss function has the same classifier as that with indicator loss function. We give analysis to NP-ERM with convex loss function and prove it＇s performance guarantees. An example of complexity penalty pair about convex loss function risk in terms of Rademacher averages is studied, which produces a tight PAC bound of the NP-ERM with convex loss function.
基金supported by the National Natural Science Foundation of China (60972152)Northwestern Polytechnical University Foun dations for Fundamental Research (JC201027 JC20100223)
文摘The problem of distributed detection fusion using multiple sensors for remote underwater target detection is studied. Considering that multiple access channel （MAC） schemes are able to offer high efficiency in bandwidth usage and consume less energy than the parallel access channel （PAC）, the MAC scheme is introduced into the underwater target detection field. The model of underwater distributed detection fusion based on MAC schemes is established. A new method for detection fusion of MAC based on deflection coefficient maximization （DCM） and Neyman-Pearson （NP） rule is proposed. Under the power constraint of local sensors, this paper uses the DCM theory to derive the optimal weight coefficients and offsets. The closed-form expressions of detection probability and false alarm probability for fusion systems are obtained. The optimal detection performance of fusion systems is analyzed and deeply researched. Both the theory analysis and simulation experiments indicate that the proposed method could improve the detection performance and decrease the error probability effectively under power constraints of local sensors and low signal to noise ratio.
基金Project supported by the National Natural Science Foundation of China and the Doctoral Programme Foundation.
文摘The stability of testing hypotheses is discussed.Differing from the usual tests measured by Neyman-Pearson lemma,the regret and correction of the tests are considered.After the decision is made based on the observations X1,X2,...,Xn,one more piece of datum Xn+1 is picked and the test is done again in the same way but based on X1,X2,...,Xn,Xn+1.There are three situations;(i) The previous decision is right but the new decision is wrong; (ii) the previous decision is wrong but the new decision is right; (iii) both of them are right or both of them are wrong.Of course,it is desired that the probability of the occurrence of (i) is as small as possible and the probability of the occurrence of (ii) is as large as possible.Since the sample size is sometimes not chosen very precisely after the type Ⅰ error and the type Ⅱ error are determined in practice,it seems more urgent to consider the above problem.Some optimal plans are also given.
基金Sponsored by the National Natural Science Foundation of China(60232010)
文摘The performance of a distributed Neyman-Pearson detection system is considered with the decision rules of the sensors given and the decisions from different sensors being mutually independent conditioned on both hypothese. To achieve the better performance at the fusion center for a general detection system of n 〉 3 sensor configuration, the necessary and sufficient conditions are derived by comparing the probability of detec- tion at the fusion center with that of each of the sensors, with the constraint that the probability of false alarm at the fusion center is equal to that of the sensor. The conditions are related with the performances of the sensors and using the results we can predict the performance at the fusion center of a distributed detection system and can choose appropriate sensors to construct efficient distributed detection systems.
文摘For the two side truncated distribution family: dPθ(x) = f(x;θ1θ2)I(θ≤ x≤θ2)dx, where θ=(θ1,θ2),θ < θ2,chen & Fu studied one side asymptotic efficiency of the estimator for parameter hation g(θ) = c1θ1 + C2θ2, they pointed out that when c1c2≥0, there exist one side asymptotic efficient estimators for g(θ); when c1c2 < 0, the estimator they proposed is not asymptotically efficient. Then they put forward a question: Is there any other asymptotically efficient estimator for g(θ) when c1c2 <0? In this paper, we study this problem, we prove that when the distribution under consideration is uniform distribution with location and scale parameters, there does not exist one side asymptotically efficient estimators for the scale parameter.
基金Supported by the National Natural Science Foundation of China under Grant No.60972152
文摘In order to solve the distributed detection fusion problem of underwater target detection, when the signal to noise ratio (SNR) of the acoustic channel is low, a new strategy for united detection fusion and communication using multiple sensors was proposed. The performance of detection fusion was studied and compared based on the Neyman-Pearson principle when the binary phase shift keying (BPSK) and on-off keying (OOK) modes were used by the local sensors. The comparative simulation and analysis between the optimal likelihood ratio test and the proposed strategy was completed, and both the theoretical analysis and simulation indicate that using the proposed new strategy could improve the detection performance effectively. In theory, the proposed strategy of united detection fusion and communication is of great significance to the establishment of an underwater target detection system.
