Question $4$ Elementary properties of $2-$norm regularized logistic regression $(30$ points, $6$ points for each subproblem$)$ Consider minimizing J$($w$)=($w$,$ Dtrain$)+$ $$w$22,(2)$ where $($w$,$ Dtrain$)=1|$D$|$ X i in D log yix T i w $(3)$ is the average log$-$likelihood on data set D$,$ for yi in $\{1,+1\}.$ Answer the following true$/$false questions and justify your answers. $1.$ J$($w$)$ has multiple locally optimal solutions? $2.$ Let w$=$ arg minw J$($w$)$ be a global optimum. w$$ is sparse $($has many zero entries$)?3.$ If the training data is linearly separable, then some weights wj might become infinite if $=0?4.($w$,$ Dtrain$)$ always increases as we increase $?5.($w$,$ Dtest$)$ always increases as we increase