【无标题】

机器学习第五次作业

6.1

由第一次检测:
P(⊕∣cancer)P(cancer)=0.0078P(⊕∣cancer)P(cancer)=0.0078P(⊕∣cancer)P(cancer)=0.0078
P(⊕∣¬cancer)P(¬cancer)=0.0298P(⊕∣\neg cancer)P(\neg cancer)=0.0298P(⊕∣¬cancer)P(¬cancer)=0.0298、

将第一次检测结果作为新的先验概率,归一化得到:
P(cancer∣⊕)=0.0078/0.0376=0.2074P(cancer∣⊕)=0.0078/0.0376=0.2074P(cancer∣⊕)=0.0078/0.0376=0.2074
P(¬cancer∣⊕)=0.0298/0.0376=0.7926P(\neg cancer∣⊕)=0.0298/0.0376=0.7926P(¬cancer∣⊕)=0.0298/0.0376=0.7926

第二次检测的后验概率:
P(cancer∣⊕,⊕)=P(⊕∣cancer)∗P(cancer∣⊕)=.098∗0.2074=0.2033P(cancer∣⊕,⊕)=P(⊕∣cancer)*P(cancer∣⊕)=.098*0.2074=0.2033P(cancer∣⊕,⊕)=P(⊕∣cancer)∗P(cancer∣⊕)=.098∗0.2074=0.2033
P(¬cancer∣⊕,⊕)=P(⊕∣¬cancer)∗P(¬cancer∣⊕)=0.03∗0.7926=0.0238P(\neg cancer∣⊕,⊕)=P(⊕∣\neg cancer)*P(\neg cancer∣⊕)=0.03*0.7926=0.0238P(¬cancer∣⊕,⊕)=P(⊕∣¬cancer)∗P(¬cancer∣⊕)=0.03∗0.7926=0.0238

归一化得:
P(cancer∣⊕,⊕)=0.2033/0.2271=0.8952P(cancer∣⊕,⊕)=0.2033/0.2271=0.8952P(cancer∣⊕,⊕)=0.2033/0.2271=0.8952
P(¬cancer∣⊕,⊕)=0.0238/0.2271=0.1048P(\neg cancer∣⊕,⊕)=0.0238/0.2271=0.1048P(¬cancer∣⊕,⊕)=0.0238/0.2271=0.1048

6.2

根据贝叶斯公式:
P(cancer∣⊕)=P(⊕∣cancer)∗P(cancer)P(⊕)=P(⊕∣cancer)∗P(cancer)P(⊕∣cancer)P(cancer)+P(⊕∣¬cancer)P(¬cancer)=1P(⊕∣cancer)P(cancer)+P(⊕∣¬cancer)P(¬cancer)P(⊕∣cancer)∗P(cancer)=11+P(⊕∣¬cancer)P(¬cancer)P(⊕∣cancer)∗P(cancer)P(cancer∣⊕)=\frac{P(⊕∣cancer)*P(cancer)}{P(⊕)}\\=\frac{P(⊕∣cancer)*P(cancer)}{P(⊕∣cancer)P(cancer)+P(⊕∣\neg cancer)P(\neg cancer)}\\=\frac{1}{\frac{P(⊕∣cancer)P(cancer)+P(⊕∣\neg cancer)P(\neg cancer)}{P(⊕∣cancer)*P(cancer)}}\\=\frac{1}{1+\frac{P(⊕∣\neg cancer)P(\neg cancer)}{P(⊕∣cancer)*P(cancer)}}P(cancer∣⊕)=P(⊕)P(⊕∣cancer)∗P(cancer)=P(⊕∣cancer)P(cancer)+P(⊕∣¬cancer)P(¬cancer)P(⊕∣cancer)∗P(cancer)=P(⊕∣cancer)∗P(cancer)P(⊕∣cancer)P(cancer)+P(⊕∣¬cancer)P(¬cancer)1=1+P(⊕∣cancer)∗P(cancer)P(⊕∣¬cancer)P(¬cancer)1

而将P(⊕∣cancer)P(cancer)P(⊕∣cancer)P(cancer)P(⊕∣cancer)P(cancer)和P(⊕∣¬cancer)P(¬cancer)P(⊕∣\neg cancer)P(\neg cancer)P(⊕∣¬cancer)P(¬cancer) 归一化,得到的正是P(⊕∣cancer)P(cancer)P(⊕)\frac{P(⊕∣cancer)P(cancer)}{P(⊕)}P(⊕)P(⊕∣cancer)P(cancer)和P(⊕∣¬cancer)P(¬cancer)P(⊕)\frac{P(⊕∣\neg cancer)P(\neg cancer)}{P(⊕)}P(⊕)P(⊕∣¬cancer)P(¬cancer),而前者正是P(cancer∣⊕)P(cancer∣⊕)P(cancer∣⊕),因此这样是正确的

相关推荐
大模型任我行2 小时前
复旦:LLM隐式推理SIM-CoT
人工智能·语言模型·自然语言处理·论文笔记
tomlone2 小时前
AI大模型核心概念
人工智能
西望云天2 小时前
The 2024 ICPC Asia Nanjing Regional Contest(2024南京区域赛EJKBG)
数据结构·算法·icpc
10岁的博客3 小时前
容器化安装新玩法
算法
不会算法的小灰3 小时前
HTML简单入门—— 基础标签与路径解析
前端·算法·html
可触的未来,发芽的智生3 小时前
触摸未来2025.10.06:声之密语从生理构造到神经网络的声音智能革命
人工智能·python·神经网络·机器学习·架构
动能小子ohhh3 小时前
AI智能体(Agent)大模型入门【6】--编写fasteAPI后端请求接口实现页面聊天
人工智能·python·深度学习·ai编程
SCBAiotAigc3 小时前
huggingface里的数据集如何下载呢?
人工智能·python
flashlight_hi4 小时前
LeetCode 分类刷题:1901. 寻找峰值 II
python·算法·leetcode