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
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.
