决策树.选择分割对象的阈值 [英] Decision trees. Choosing thresholds to split objects

问题描述

如果我正确理解了此，则一组呈现了对象(即要素数组)，我们需要将其分为2个子集.为此，我们将某些特征x _j 与阈值t _m (t _m 是m个节点的阈值)进行比较.我们使用杂质函数H()来找到分割对象的最佳方法.但是，我们如何选择t _m 的值，以及应该将哪个特征与阈值进行比较?我的意思是，我们可以选择t _m 的方法有无数种，因此我们不能只为每种可能性计算H()函数.

If I understand this correctly, a set of objects (which are arrays of features) is presented and we need to split it into 2 subsets. To do that we compare some feature x_j to a threshold t_m (t_m is the threshold at m node). We use an impurity function H() to find the best way to split the objects. But how do we choose the values of t_m and which feature should be compared to the thresholds? I mean, there is an infinite number of ways we can choose t_m so we can't just compute H() function for each possibility.

推荐答案

在这些

In Page 18 of these slides, two methods are introduced to choose the splitting threshold for a numerical attribute X.

方法1:

• 根据X将数据排序为{x_1，...，x_m}
• 考虑x_i +(x_ {i + 1}-x_i)/2形式的分割点

方法2:

假设X是一个实值变量

• 将IG(Y | X:t)定义为H(Y)-H(Y | X:t)

• Define IG(Y|X:t) as H(Y) - H(Y|X:t)

定义H(Y | X:t)= H(Y | X = t)P(X> = t)

Define H(Y|X:t) = H(Y|X < t) P(X < t) + H(Y|X >= t) P(X >= t)

• IG(Y | X:t)是预测所有Y的信息增益 知道X是否大于或小于t

• IG(Y|X:t) is the information gain for predicting Y if all you know is whether X is greater than or less than t

然后定义IG ^ *(Y | X)= max_t IG(Y | X:t)

Then define IG^*(Y|X) = max_t IG(Y|X:t)

对于每个实值属性，请使用IG *(Y | X)来评估其作为拆分的适用性

For each real-valued attribute, use IG*(Y|X) for assessing its suitability as a split

注意，可能会在一个属性上多次拆分， 具有不同的阈值

Note, may split on an attribute multiple times, with different thresholds

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