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 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
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.
