argmax

function that returns the input that maximizes the expression.

finding argmax

Typical maximization system. Take derivative, set it to 0, solve, plug in, solve. THis is pretty bad during times are not differentiable.

We take steps following the direction

\begin{equation} \theta_{1j} = \theta_{0j} + \eta \pdv{LL(\theta_{0})}{\theta_{0j}} \end{equation}