線形ウィークラーナーによるアンサンブル学習の汎化誤差の解析

抄録

Generalization ability of the ensemble learning through linear simple perceptron is analyzed by using the stochastic mechanics method. The element of the initial connection weight is given by a Gaussian random number so that the ensemble learning is performed effectively. To analyze the effect of number of the perceptrons used in the ensemble learning, linear simple perceptrons are taken into account. Additive noise for the teacher's output or student's output is considered. Each element of teacher and student networks are considered to be initialized by Gaussian distibution of zero mean and unit valiance. From the analytical results, we found that in the limit of K is infinity, the generalization error of ensemble learning with the K linear perceptrons are a half of that of the single perceptron. For finite number of perceptrons, the generalization error converges to the value of a half of the single perceptron's one with 1/K when no noise is added. Asymptotic property of the ensemble learning is not effective for teacher's output noise, however, from analysis of dynamics of the generalization error, it is found that the ensemble learning is effective at the early stage of the learning.