李宏毅2020机器学习2

10. Classification

分类应用很多，例如：
Credit scoring：Input: income, savings, profession, age, …, Output: accept or refuse
Medical Diagnosis: Input: current symptoms, age, gender, …, Output: which kind of diseases
Handwritten character recognition
Face recognition: Input: image of a face, Output: persion

10.1 Generative model 生成模型

高斯分布
贝叶斯概率
极大释然估计

11. Logistic Regression

Step 1: Function Set
$f_{w,b}(x)=P_{w,b}(C_1|x)=\sigma (z)$
$\sigma (z)=\frac{1}{1+e^{-z}}$
$z=w\cdot x+b={\sum }_i{w}_i{x}_i+b$

sigmoid 函数默认是高斯分布

Step 2: Goodness of a Function
损失函数可以判断函数的好坏

Step 3: Find the best function
梯度下降法找最佳函数

-	Logistic Regression	Linear Regression
Step 1	$$\begin{gathered} f_{w,b}(x)=\sigma ({\sum }_i{w}_i{x}_i+b) \\ \text{Output: between 0 and 1} \end{gathered}$$	$$\begin{gathered} f_{w,b}(x)={\sum }_i{w}_i{x}_i+b \\ \text{Output: any value} \end{gathered}$$
Step 2	Training data: ( x n , y ^ n ) y ^ n : 1 for class 1, 0 for class 2 L ( f ) =