学习方法的泛化能力(Generalization Error)是由该方法学习到的模型对未知数据的预测能力,是学习方法本质上重要的性质。现实中采用最多的办法是通过测试泛化误差来评价学习方法的泛化能力。泛化误差界刻画了学习算法的经验风险与期望风险之间偏差和收敛速度。一个机器学习的泛化误差(Generalization Error),是一个描述学生机器在从样品数据中学习之后,离教师机器之间的差距的函数。

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Ensembles, as a widely used and effective technique in the machine learning community, succeed within a key element -- "diversity." The relationship between diversity and generalization, unfortunately, is not entirely understood and remains an open research issue. To reveal the effect of diversity on the generalization of classification ensembles, we investigate three issues on diversity, i.e., the measurement of diversity, the relationship between the proposed diversity and the generalization error, and the utilization of this relationship for ensemble pruning. In the diversity measurement, we measure diversity by error decomposition inspired by regression ensembles, which decomposes the error of classification ensembles into accuracy and diversity. Then we formulate the relationship between the measured diversity and ensemble performance through the theorem of margin and generalization and observe that the generalization error is reduced effectively only when the measured diversity is increased in a few specific ranges, while in other ranges larger diversity is less beneficial to increasing the generalization of an ensemble. Besides, we propose two pruning methods based on diversity management to utilize this relationship, which could increase diversity appropriately and shrink the size of the ensemble without much-decreasing performance. Empirical results validate the reasonableness of the proposed relationship between diversity and ensemble generalization error and the effectiveness of the proposed pruning methods.

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Ensembles, as a widely used and effective technique in the machine learning community, succeed within a key element -- "diversity." The relationship between diversity and generalization, unfortunately, is not entirely understood and remains an open research issue. To reveal the effect of diversity on the generalization of classification ensembles, we investigate three issues on diversity, i.e., the measurement of diversity, the relationship between the proposed diversity and the generalization error, and the utilization of this relationship for ensemble pruning. In the diversity measurement, we measure diversity by error decomposition inspired by regression ensembles, which decomposes the error of classification ensembles into accuracy and diversity. Then we formulate the relationship between the measured diversity and ensemble performance through the theorem of margin and generalization and observe that the generalization error is reduced effectively only when the measured diversity is increased in a few specific ranges, while in other ranges larger diversity is less beneficial to increasing the generalization of an ensemble. Besides, we propose two pruning methods based on diversity management to utilize this relationship, which could increase diversity appropriately and shrink the size of the ensemble without much-decreasing performance. Empirical results validate the reasonableness of the proposed relationship between diversity and ensemble generalization error and the effectiveness of the proposed pruning methods.

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