On weak base Hypotheses and their implications for boosting regression and classification
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弱基假设及其对提升回归与分类的含义
- 研究问题
- 提升过程中，基学习器优于随机猜测的优势会否消失或保持正下界，这一性质对训练误差、预测误差和正则化有何影响？
- 方法与思路
- 作者先分析回归中与 AdaBoost 类似的程序，再研究常用基假设相对随机猜测的优势下界及其对分类提升的含义。
- 材料陈述的贡献
- 摘要称，对几乎所有可能样本实现和多数常用基假设，该优势保持正下界；持续提升未必有利，正则化可能仍然必要。
- 阅读关注点
- 应核对样本实现的概率限定、所覆盖的基假设类别及优势下界定义，并检查这些结果如何支持预测误差和正则化结论。
- 阅读边界
- 仅据版本未注明的索引摘要；具体基假设、误差界及停止规则未说明，不能把优势下界解释为预测误差持续下降。
原文摘要
When studying the training error and the prediction error for boosting, it is often assumed that the hypotheses returned by the base learner are weakly accurate, or are able to beat a random guesser by a certain amount of difference. It has been an open question how much this difference can be, whether it will eventually disappear in the boosting process or be bounded by a positive amount. This question is crucial for the behavior of both the training error and the prediction error. In this paper we study this problem and show affirmatively that the amount of improvement over the random guesser will be at least a positive amount for almost all possible sample realizations and for most of the commonly used base hypotheses. This has a number of implications for the prediction error, including, for example, that boosting forever may not be good and regularization may be necessary. The problem is studied by first considering an analog of AdaBoost in regression, where we study similar properties and find that, for good performance, one cannot hope to avoid regularization by just adopting the boosting device to regression.