Equations

\[ \begin{eqnarray} \underset{\theta}{\operatorname{argmin}} D_{KL}[p^*(Y|X) || p(Y|X;\theta)] &=& \sum_{(x,y) \in D} p^*(y|x) \cdot \log \frac{p^*(y|x)}{p(y|x,\theta)} \\\\\\ &=& \sum_{x \in D} p^*(y|x)[\log p^*(y|x) - \log p(y|x,\theta)] \\\\\\ &=& \sum_{x \in D} p^*(y|x) \log p^*(y|x) - \sum_{x \in D} p^*(y|x) \log p(y|x,\theta) \\\\\\ &=& - \sum_{x \in D} p^*(y|x) \log p(y|x,\theta) \\\\\\ &=& - \sum_{(x,t) \in D} t \cdot \log p(y|x,\theta) \end{eqnarray} \] \[ x^2 \]

\[ x^2 \] \( y^2 \) \( y^2 \)

$$ z^2 $$