Classification Model

Description:

• To classify the data into 1 of possible catergories

Boolean classification:

• We turn the outcome to $\pm 1$ which denotes positive and negative
• Then round up/down to the nearest -1 or 1
• We can then have :
  • True positive, $y=\hat{y}=+1$
  • True negative, $y=\hat{y}=-1$
  • False positive, $y=-1$ and $\hat{y}=1$ Type 1 Error
    • False positive rate = false positive / total real negative
  • False negative, $y=1$ and $\hat{y}=-1$ Type 2 Error
    • false negative rate = false negative / total real positive
  • Error rate is defined by (false positive + false negative)/ total observations

Least Square Classification

Multi-class Classification

Model-based Classification

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Nearest Neighbor for Classification

Binary classification:

• Given:
  • an input space $\chi$
  • an unknown disribution $D$ over $\chi \times \{-1,1\}$
• Learning: find a function $f$ minizing $E_{(x,y)}\sim D[f(x)\ne y]$
• Binary Classification with Linear Models