机器学习基石 - Feasibility of Learning

机器学习基石上 (Machine Learning Foundations)—Mathematical Foundations
Hsuan-Tien Lin, 林轩田，副教授 (Associate Professor)，资讯工程学系 (Computer Science and Information Engineering)

Feasibility of Learning

Learning is Impossible?

• Two Controversial Answers 多种合理的方式得到不同的答案

• no-free-lunch problems

Probability to the Rescue

• Inferring Something Unknown → sample

• 样本(in-sample)的概率与整体(out-of-sample)的概率大概是接近的

• Hoeffding’s Inequality

  • 
  • 

Connection to Learning

• 抓弹珠类比学习
  

  • 抓的一把弹珠是已知数据
  • 橙色的代表错误
  • 抽样测试，测试集上的正确率

• 增加部件
  

• 公式表述
  

• Verification

  • Verification of One h
    
  • The Verification Flow
    

Connection to Real Learning

• BAD sample: Ein$E_{in}$ and Eout$E_{out}$ far away (can get worse when involving choice)

• BAD Data for One h: Ein(h)$E_{in}(h)$ and Eout(h)$E_{out}(h)$ far away

  • 不好的几率很小
    

• BAD Data for Many h

  • 
  • for M$M$ hypotheses, bound of PD[BADD]${\mathbb{P}}_{\mathcal{D}}[BAD\mathcal{D}]$
    

• The Statistical Learning Flow
  

learning possible if |H|$|\mathcal{H}|$ finite and Ein(g)$E_{in}(g)$ small