Classification week2: logistic regression classifier 笔记

时间:2023-03-09 01:01:08
Classification week2: logistic regression classifier 笔记

华盛顿大学 machine learning: Classification 笔记。

linear classifier 线性分类器

  Classification week2: logistic regression classifier 笔记

  多项式:

  Classification week2: logistic regression classifier 笔记

Logistic regression & 概率模型

   Classification week2: logistic regression classifier 笔记

  P(y = +1 | x) = ?

  使用 logistic函数

    Classification week2: logistic regression classifier 笔记

      Classification week2: logistic regression classifier 笔记    

  Classification week2: logistic regression classifier 笔记

这个概率模型怎么来的?

  (李航《统计学习方法》)

Classification week2: logistic regression classifier 笔记

  即

              Classification week2: logistic regression classifier 笔记

  考虑对输入x进行分类的线性函数 w x,其值域为实数域,线性函数wx可转换为概率:

               Classification week2: logistic regression classifier 笔记

  这时,线性函数值越接近正无穷,概率值就越接近1;线性函数值越接近负无穷,

概率值就越接近0。

  这种概率描述适用于这样的情况:即在P=0或P=1附近,P对X的变化不敏感。这种概率模型的应用场景主要是分类。

极大似然估计模型参数w

Maximize Likelihood Estimation(MLE) 极大似然估计

  Classification week2: logistic regression classifier 笔记

         Classification week2: logistic regression classifier 笔记

    即 选择使  l(w) 最大的参数 w。

  对 l(w) 取对数:

  Classification week2: logistic regression classifier 笔记

   展开得

    Classification week2: logistic regression classifier 笔记

梯度下降(Gradient-descent):

  Classification week2: logistic regression classifier 笔记

防止过拟合:

Classification week2: logistic regression classifier 笔记

  即

   Classification week2: logistic regression classifier 笔记

  梯度下降

  Classification week2: logistic regression classifier 笔记