Given X, we want $\hat{y}=P(y = 1|X)$ $0 \leq \hat{y} \leq 1$

Parameters: $w \in R^{n_{x}}, b \in R$

Output (Activation): $\hat{y}^{(i)} = a^{(i)} = \sigma (w^{T}x^{(i)} + b)$

Given [(x^{(1)}, y^{(1)}), (x^{(2)}, y^{(2)}), ..., (x^{(m)}, y^{(m)})], we want $\hat{y}^{i} \approx y^{i}$

$\sigma(z^{(i)}) = \frac{1}{1 + e^{-z^{(i)}}}$

If z is large positive, $\sigma(z^{(i)}) \approx \frac{1}{1 + 0} = 1$

If z is large negative, $\sigma(z^{(i)}) \approx \frac{1}{1 + Big Num} \approx 0$