GBDT与LR融合提升广告点击率预估模型
1GBDT和LR融合
LR模型是线性的,处理能力有限,所以要想处理大规模问题,需要大量人力进行特征工程,组合相似的特征,例如user和Ad维度的特征进行组合。
GDBT天然适合做特征提取,因为GBDT由回归树组成所以, 每棵回归树就是天然的有区分性的特征及组合特征,然后给LR模型训练,提高点击率预估模型(很多公司技术发展应用过,本人认为dnn才是趋势)。
例如,输入样本x,GBDT模型得到两颗树tree1和tree2,遍历两颗树,每个叶子节点都是LR模型的一个维度特征,在求和每个叶子*权重及时LR模型的分类结果。
![](https://images2015.cnblogs.com/blog/751250/201705/751250-20170506222710382-1525511395.png)
2广告长尾性
1)gbdt和随机森林rf的对比:
rf主要选择对大多数样本有区分度的特征;gbdt的过程,前面树针对大多数样本有区分 ,后面树针对残差依然较大的样本,即针少数的对长尾样本。更适合ctr模型预估。
2)针对广告的长尾性,广告id这个特征就很重要,比如:某少量长尾用户就喜欢点某类广告主的广告。
方案:分别针对ID类和非ID类建树,ID类树:用于发现曝光充分的ID对应的有区分性的特征及组合特征;非ID类树:用于曝光较少的广告。
![](https://images2015.cnblogs.com/blog/751250/201705/751250-20170506222737007-1860770754.png)
3gbdt得到的特征维度
维度会降低,总维度是所有叶子节点数之和。
4gdbt模型原理
1)BT回归树
年龄预测:简单起见训练集只有4个人,A,B,C,D,他们的年龄分别是14,16,24,26。其中A、B分别是高一和高三学生;C,D分别是应届毕业生和工作两年的员工。
1BT回归树:显然容易过拟合,特征太细了,只要叶子允许够多可以达到百分百的准确率,但性能并不好。
![](https://images2015.cnblogs.com/blog/751250/201705/751250-20170506222801226-730625540.png)
2)GDBT模型
(1)最小化均方误差特,确定特征:购物金额的分割点:
![](https://images2015.cnblogs.com/blog/751250/201705/751250-20170506222815586-1896396752.png)
(2)计算残差=预测值-真实值,真实值是叶子节点均值,特征:百度知道提问:
![](https://images2015.cnblogs.com/blog/751250/201705/751250-20170506222833226-2068373417.png)
(3)残差为0,停止迭代,输出预测结果,真实值=初始值+残差之和
A: 14岁高一学生,购物较少,经常问学长问题;预测年龄A = 15 – 1 = 14
B: 16岁高三学生;购物较少,经常被学弟问问题;预测年龄B = 15 + 1 = 16
C: 24岁应届毕业生;购物较多,经常问师兄问题;预测年龄C = 25 – 1 = 24
D: 26岁工作两年员工;购物较多,经常被师弟问问题;预测年龄D = 25 + 1 = 26
5 GDBT和Adaboost公式算法层级的解释
Ada boost是根据分错的样本
GDBT是拟合梯度(残差)
(1)梯度下降和梯度提升的区别联系
梯度下降:参数=迭代的增量累加和,特征维度
梯度提升:参数=迭代的函数增量累加和,分类器(回归树or罗辑回归)维度
所以boosting就是一个加法模型![](data:image/png;base64,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)
![](https://images2017.cnblogs.com/blog/751250/201708/751250-20170819142642537-1432712320.jpg)
(2) gradient boosting tree (Gradient Boosting = Gradient Descent + Boosting)
目标函数:![](data:image/png;base64,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)
梯度:对分类器求导数
![](https://images2017.cnblogs.com/blog/751250/201708/751250-20170819142829193-1744905438.jpg)
eg:
1 m个样本集:
,label改写为残差
(残差就是目标函数最小化1/2*
的梯度)
2 训练,相当于回归树拟合梯度,最后模型一个函数加法模型
(3) Adaboost
CART回归树分类器对样本训练分类,等到分类器误差
1根据分类器误差计算每个分类器对权重
2根据分类器误差计算每个样本的权重
输出加法模型,累加每个分类器权重*分类器函数
![](https://images2017.cnblogs.com/blog/751250/201708/751250-20170819142905271-1106285231.jpg)
总结:
原则1:没有免费的午餐,没有一个模型在所有数据集上优于另一个模型。
原则2:剃姆刀原则,效果一样的情况下选择简单的模型。eg LR和GDBT效果一样的情况下,尽量选择LR。
参考