摘要
Many researchers have worked on the ex- planation of AdaBoost＇s good experimental results in theory. Some work give an upper bound of generaliza- tion error in terms of the margin distribution function, while Breiman gave a sharper generalization error bound based on minimum margin. He also developed the arc- gv algorithm to maximize the minimum margin, then made the minimum margin larger than AdaBoost. How- ever, its empirical results are even worse than AdaBoost. Therefore, is the minimum margin bound not practi- cal？ This paper gives a new concept called Equilibrium margin （Emargin） and proves a new generalization er- ror bound using Emargin, which is always better than minimum margin bound. In addition, we show Emargin is a good indicator of generalization. Then, we conduct experiments showing that the Emargin of AdaBoost is larger than arc-gv, but the generalization error of Ada- Boost is usually better.
Many researchers have worked on the ex- planation of AdaBoost＇s good experimental results in theory. Some work give an upper bound of generaliza- tion error in terms of the margin distribution function, while Breiman gave a sharper generalization error bound based on minimum margin. He also developed the arc- gv algorithm to maximize the minimum margin, then made the minimum margin larger than AdaBoost. How- ever, its empirical results are even worse than AdaBoost. Therefore, is the minimum margin bound not practi- cal？ This paper gives a new concept called Equilibrium margin （Emargin） and proves a new generalization er- ror bound using Emargin, which is always better than minimum margin bound. In addition, we show Emargin is a good indicator of generalization. Then, we conduct experiments showing that the Emargin of AdaBoost is larger than arc-gv, but the generalization error of Ada- Boost is usually better.
