## Learning with Different Output Space $\gamma$

### Binary classification

• Y = {−1, +1}

• ### Multiclass Classification

• classify US coins (1c, 5c, 10c, 25c) by (size, mass)
• $\gamma = {1c,5c,10c,25c}$,or $\gamma = {1,2,··· ,K}$ (abstractly)
• binary classification: special case with K =2
• ### Regression

• $\gamma = \mathbb{R}$ or $\gamma = [lower, upper] \subset \mathbb{R}$ (bounded regression)

### Structured Learning: Sequence Tagging Problem

• a fancy but complicated learning problem
• sentence -> structure (class of each word)
• $\gamma = \{PVN,PVP,NVN,PV,···\}$, not including VVVVV
• huge multiclass classification problem ($structure \equiv hyperclass$) without explicit class definition

## Learning with Different Data Label $y_n$

### Supervised learning

• every $x_n$ comes with corresponding $y_n$

### Unsupervised learning

• clustering
• articles -> topics
• consumer profiles -> consumer groups
• density estimation: {xn} -> density(x)
• i.e. traffic reports with location -> dangerous areas
• outlier detection: {xn} -> unusual(x)
• i.e. Internet logs -> intrusion alert

### Semi-supervised learning

• leverage unlabeled data to avoid expensive labeling
• ### Reinforcement Learning

• Teach Your Dog: Say Sit Down
• cannot easily show the dog that $y_n$ = sit when $x_n$ = sit down
• but can punish to say $\hat{y_n}$ = pee is wrong
• but can reward to say $\hat{y_n}$ = sit is good
• learn with partial/implicit information (often sequentially)

## Learning with different Protocol $f \rightarrow (x_n,y_n)$

### Batch Learning

• batch supervised multiclass classification: learn from all known data

### Online Learning:

• hypothesis improves through receiving data instances sequentially

### Active Learning: Learning by ‘Asking’

• improve hypothesis with fewer labels (hopefully) by asking questions strategically

## Learning with different Input Space $\chi$

• concrete features: each dimension of $\chi \in \mathbb{R}$ represents sophisticated physical meaning
• Raw Features
• simple physical meaning; thus more difficult for ML than concrete features
• often need human or machines to convert to concrete ones
• Abstract Features: again need feature conversion/extraction/construction
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