math

$$ e^{i \pi} = -1 $$

Cross Entropy Binary Cross Entropy Given a dataset $D = \{ (x_1, y_1), \cdots, (x_n, y_n) \}$ where $x_i \in \mathbb{R}^d$ and $y_i \in \{ 1,0 \}$. Let $h: \mathbb{R}^d \rightarrow [0,1]$ be the function in hypothesis set and $\hat{y_i} = h(x_i)$ for all $i=1,\cdots, n$. Since we have $$ p(y_i=1|x_i) = \left\{\begin{array}{cc} h(x_i) & \text{ if } y_i = 1 \\ 1-h(x_i) & \text{ if } y_i = 0 \end{array} \right....