Huber Loss is given as follows:
I'd like to proof $\gamma=median\{y_1,...y_N \}$ minimizes the Huber Loss so i've taken its first derivate for $\gamma\neq y_i$:
I've tried to proof that first derivate change its signal before and after the median, i mean $\frac{\partial R}{\partial \gamma}<0$ when $\lambda< median$ and $\frac{\partial R}{\partial \gamma}>0$ when $\lambda > median$ but i didnt get any satisfactory solution.
