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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)

Types of Learning

Learning with Different Output Space

• Binary Classification (二元分类)
• Multiclass Classification 输出多个类别 （是非题变为选择题）
• Regression (回归分析): deeply studied in statistics
• Structured Learning 结构化学习 (huge multiclass classification problem)
• 

Learning with Different Data Label $y_n$

关于监督学习和非监督学习

• Multiclass Classification 下的几种情况

  

• Supervised Learning: every $\mathbf x_n$ comes with corresponding $y_n$

  每个输入都知道对应的正确输出

• Unsupervised: Learning without $y_n$

  • clustering (聚类)
  • density estimation (密度分析)
  • outlier detection (离群点分析)

• Semi-supervised: Learn with some $y_n$

  • leverage unlabeled data to avoid ‘expensive’ labeling
  • 标记的代价可能很大，只能做一部分

Reinforcement Learning (增强学习)

• a very different but natural way of learning

• 惩罚错误的行为，奖励正确的行为

• 例子
  
• learn with partial/implicit information (often sequentially) (一个一个的来学习)

Learning with Different Protocol $f\Rightarrow (\mathbf x_n,y_n)$

和机器的沟通方式

• Batch Learning: 喂给机器一批一批的数据 (duck feeding)

  监督学习、非监督学习

• Online Learning: 一个一个的来 (sequentially)

  PLA、增强学习

• Active Learning: 主动的去学习 (ask questions)

  • query the $y_n$ of the chosen $\mathbf x_n$
  • improve hypothesis with fewer labels (hopefully) by asking questions strategically
  • 机器无法识别时，让机器自己来问，需要标记的可能就少一些

• 总结

  

Learning with Different Input Space $\mathcal X$

Concrete Features

• each dimension of $\mathcal X \subseteq \mathbb R^d$ represents sophisticated physical meaning

• 具体的东西，可以计算，预先有人类智慧的加工

• the easy ones for ML

Raw Features

• 更为抽象，包含很多细节 simple physical meaning

• like image pixels, speech signal, etc.

• often need human or machines to convert to concrete ones

• feature engineer (特征工程) 提取出哪些特征给机器比较好

Abstract Features

• 需要机器自己去学到特征

• no physical meaning

• need feature conversion/extraction/construction

• 例如只有一些编号的对应关系

思考题