\subsection{Non-Linear Least Squares}
Find $\vec{x}^* = \text{argmax}\; \P(\vec{x} | \vec{z}) = \argmin{}(-\log(\P(\vec{x}|\vec{z})))$

\bi{Gauss-Newton} Need func $F$ and its Jacobian (or derivative) $DF$
\rmvspace[0.3]
% TODO: Error propagation laws
{\small
    \begin{minted}[
    breaklines,
    breakindentnchars=2,
]{python}
def gauss_newton(x: np.ndarray, F, DF, tol=1e-6):
    s = np.linalg.lstsq(DF(x), F(x))[0] # least sq.
    x = x-s; k = 1
    while np.linalg.norm(s) > tol * np.linalg.norm(x):
        s = np.linalg.lstsq(DF(x), F(x))[0]
        x = x-s; k += 1 # k optional for max iter
    return x, k
\end{minted}
}
\rmvspace[0.4]

\bi{Levenberg-Marquardt}
Minimize $||F(x^{(k)}) + DF(x^{(k)})||^2 + \lambda||s||^2$,
with $s = \lambda_k DF(x^{(k)})$, $\lambda_k$ is called the \textit{learning rate}
% TODO: Do we need these?

\bi{Local Param.}