1 逻辑回归
逻辑回归(Logistics Regression)是机器学习中的一种分类模型,逻辑回归是一种分类算法,虽然名字中带有回归,但是它与回归之间有一定的区别。由于算法的简单和高效,在实际中应用非常广泛。
1.1 逻辑回归的应用场景
![](https://img8.php1.cn/3cdc5/1e87f/711/b6f9b8fabb088020.png)
1.2 逻辑回归的原理
1.2.1 输入
![](https://img8.php1.cn/3cdc5/1e87f/711/2cdbedc02a161041.png)
1.2.2 激活函数
![](https://img8.php1.cn/3cdc5/1e87f/711/6c29c531d58408cd.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2g0MjQxNzc4,size_16,color_FFFFFF,t_70)
![](https://img8.php1.cn/3cdc5/1e87f/711/2df5de6b64102478.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2g0MjQxNzc4,size_16,color_FFFFFF,t_70)
![](https://img8.php1.cn/3cdc5/1e87f/711/e7bb131ae517f89c.png)
![](https://img8.php1.cn/3cdc5/1e87f/711/c0f40f0f384f67bb.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2g0MjQxNzc4,size_16,color_FFFFFF,t_70)
1.3 损失以及优化
1.3.1 损失
逻辑回归的损失,称之为对数似然损失,公式如下:
![](https://img8.php1.cn/3cdc5/1e87f/711/c94451cab40380c7.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2g0MjQxNzc4,size_16,color_FFFFFF,t_70)
![](https://img8.php1.cn/3cdc5/1e87f/711/984a585462beca76.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2g0MjQxNzc4,size_16,color_FFFFFF,t_70)
![](https://img8.php1.cn/3cdc5/1e87f/711/5de03b8a34d312cd.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2g0MjQxNzc4,size_16,color_FFFFFF,t_70)
1.3.2 优化
![](https://img8.php1.cn/3cdc5/1e87f/711/0d96d5efc4fcea11.png)
1.4 逻辑回归API
![](https://img8.php1.cn/3cdc5/1e87f/711/4a80ee9ade477b42.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2g0MjQxNzc4,size_16,color_FFFFFF,t_70)
1.5 案例:癌症分类预测-良/恶性乳腺癌肿瘤预测
1.5.1 数据介绍
数据下载地址
1.5.2 使用Jupyter实现流程
Jupyter如何使用可参考 此博客:python jupyter的安装使用
![](https://img8.php1.cn/3cdc5/1e87f/711/3d1cbe775d39edaf.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2g0MjQxNzc4,size_16,color_FFFFFF,t_70)
![](https://img8.php1.cn/3cdc5/1e87f/711/3158d6a12b8f62c9.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2g0MjQxNzc4,size_16,color_FFFFFF,t_70)