Logistic Regression

Canonical model for classification. Convert real number to probability.

Essence

$$ \begin{aligned} \mathbb{R} \mapsto [0, 1](\text{Probability}) \end{aligned} $$

Sigmoid Function

$$ \begin{aligned} \sigma(z_i) = \frac{1}{1 + e^{-z_i}} \end{aligned} $$

where $$ \begin{aligned} z_i &= \underline{x_i} \cdot \underline{b} + b_0 \end{aligned} $$

Trick

$$ \begin{aligned} (\infty &\rightarrow 0) \\ &\downarrow \\ (\infty &\rightarrow 1) \\ &\downarrow \\ (0 &\rightarrow 1) \end{aligned} $$

by Jon