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(Machine Learning Foundations)—Mathematical Foundations

，副教授 (Associate Professor)，资讯工程学系 (Computer Science and Information Engineering)

Logistic Regression Problem

• logistic hypothesis: $h(\mathbf x)=\theta (\mathbf w^T \mathbf x)$
• logistic function $\theta (s)=\frac{1}{1+e^{-s}}$
• $sign(h(\mathbf x)-0.5)=sign(\mathbf w^T \mathbf x)$

Logistic Regression Error

• Likelihood of Logistic Hypothesis

  

  极大似然

• cross-entropy error

  

  在极大似然估计下，logistic方程的误差函数

Gradient of Logistic Regression Error

• Minimizing $E_{in}(\mathbf w)$

  

• PLA Revisited: Iterative Optimization

  

Gradient Descent

• Linear Approximation

  

• Simple Heuristic for Changing $\eta$

  

• Logistic Regression Algorithm