\subsection{Linear Least Squares}
\bi{Goal}: $\argmin{x \in \R^n} ||\mat{A}\vec{x} - b||^2_2$, $\mat{A}$: rows $i$-th datap. col $c$: $t_i^{c - 1}$.

\bi{Man. sol.}: comp. $M = A^\top A$, $b' = A^\top b$, then $Mx = b'$.

\bi{Prob. sol.}: $\text{argmax} \; \P(\vec{x} \divider \vec{z})$ with Maximum \dots
\begin{itemize}
    \item \bi{Likelihood} $\P(\vec{x} | \vec{z}) \propto \P(\vec{z} | \vec{x}) = \prod_{i = 1}^N \P(\vec{z}_i | \vec{x})$
    \item \bi{a Post} $\P(\vec{x} | \vec{z}) \propto \P(\vec{z} | \vec{x}) \P(\vec{x}) = \P(\vec{x}) \prod_{i = 1}^N \P(\vec{z}_i | \vec{x})$
\end{itemize}
