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Bootstrap又称自展法、自举法、自助法、靴带法 , 是统计学习中一种重采样(Resampling)技术,用来估计标准误差、置信区间和偏差
Bootstrap是现代统计学较为流行的一种统计方法,在小样本时效果很好。机器学习中的Bagging,AdaBoost等方法其实都蕴含了Boostrap的思想,在集成学习的范畴里
Bootstrap直接派生出了Bagging模型.
子样本之于样本,可以类比样本之于总体
举例
栗子:我要统计鱼塘里面的鱼的条数,怎么统计呢?假设鱼塘总共有鱼1000条,我是开了上帝视角的,但是你是不知道里面有多少。
步骤:
1. 承包鱼塘,不让别人捞鱼(规定总体分布不变)。
2. 自己捞鱼,捞100条,都打上标签(构造样本)
3. 把鱼放回鱼塘,休息一晚(使之混入整个鱼群,确保之后抽样随机)
4. 开始捞鱼,每次捞100条,数一下,自己昨天标记的鱼有多少条,占比多少(一次重采样取分布)。
5. 重复3,4步骤n次。建立分布。
(原理是中心极限定理)
假设一下,第一次重新捕鱼100条,发现里面有标记的鱼12条,记下为12%,放回去,再捕鱼100条,发现标记的为9条,记下9%,重复重复好多次之后,假设取置信区间95%,你会发现,每次捕鱼平均在10条左右有标记,所以,我们可以大致推测出鱼塘有1000条左右。其实是一个很简单的类似于一个比例问题。这也是因为提出者Efron给统计学顶级期刊投稿的时候被拒绝的理由--"太简单"。这也就解释了,为什么在小样本的时候,bootstrap效果较好,你这样想,如果我想统计大海里有多少鱼,你标记100000条也没用啊,因为实际数量太过庞大,你取的样本相比于太过渺小,最实际的就是,你下次再捕100000的时候,发现一条都没有标记,就尴尬了。。。