From a0bfa9cc94ee078b6d05200d9abaefcce7963730 Mon Sep 17 00:00:00 2001 From: benjas <909336740@qq.com> Date: Fri, 16 Apr 2021 20:42:07 +0800 Subject: [PATCH] Add. Information entropy --- .../5.决策树——每次选一边.md | 68 +++++++++++++++++- .../assets/1618575672562.png | Bin 0 -> 121008 bytes .../assets/1618575710142.png | Bin 0 -> 186757 bytes .../assets/1618576033128.png | Bin 0 -> 136484 bytes .../assets/1618576749908.png | Bin 0 -> 17241 bytes .../assets/1618576770871.png | Bin 0 -> 20637 bytes 6 files changed, 67 insertions(+), 1 deletion(-) create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1618575672562.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1618575710142.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1618576033128.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1618576749908.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1618576770871.png diff --git a/机器学习算法理论及应用/李航——统计学习方法/5.决策树——每次选一边.md b/机器学习算法理论及应用/李航——统计学习方法/5.决策树——每次选一边.md index 83509c0..ee7eb44 100644 --- a/机器学习算法理论及应用/李航——统计学习方法/5.决策树——每次选一边.md +++ b/机器学习算法理论及应用/李航——统计学习方法/5.决策树——每次选一边.md @@ -1 +1,67 @@ -# 5.决策树——每次选一边 \ No newline at end of file +# 5.决策树——每次选一边 + +Decision tree + + + +### 知识树 + +Knowledge tree + +![1618575672562](assets/1618575672562.png) + + + +### 一个小故事 + +A story + +挑苹果: + +![1618575710142](assets/1618575710142.png) + +> 根据这些特征,如颜色是否是红色、硬度是否是硬、香味是否是香,如果全部满足绝对是好苹果,或者红色+硬但是无味也是好苹果,从上图可以看出来,只要做足够的循环判断即可得到结果。 + +如下图: + +![1618576033128](assets/1618576033128.png) + +> 一步步走下来,就能挑到好苹果。这就是决策树 + +1. 最顶端的叫根节点,所有样本的预测都是从根节点开始。 +2. 每一个圆形节点表示判断,每个节点只对样本的某个属性进行判断。 +3. 圆形节点是标记节点,走到圆形节点表示判断结束,将圆形节点中的标签作为对应的预测结果。 + +如何构建决策树: + +1. 构建的决策树按顺序对每个特征进行判断(低效) +2. 每个判断节点都尽可能让一半进入A分支,另一半进入B分支(高效) + +引入新的知识,信息熵 + + + +### 信息熵 + +Information entropy + +1. 每走一步,我们都在确定苹果的好坏。 +2. 在根节点时,我们对苹果的好坏一无所知。 +3. 经过对颜色的判断后,如果是红色,我们明白好坏的概率是1/2。虽然还包含了1/2的不确定性。 +4. 如果苹果红色的前提下又硬,我们100%确定它是好苹果。此时不确定性坍塌为0。 +5. 这是一个减少不确定性的过程。 + +从整体来讲,我们希望决策树每走一步,不确定性都下降的快一些,让我们的判断步数无限小。 + +**什么是信息的不确定性?** + +就是信息熵 + +在信息论与概率统计中,熵(entropy)是表示随机变量不确定性的度量,设X是一个取有限个值的离散随机变量,其概率分布为 + +![1618576749908](assets/1618576749908.png) + +则随机变量X的熵定义为 + 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