Multiclass Classification with Softmax $(5$ points$)$ Now, consider a dataset D $=\{($x$1,$y$1),...,($xN$,$yN$)\},$ where yi in $\{1,2,...,$K$\}$ represents K classes, and xi in Rd$.$ The conditional probability of observing yi $=$ k given xi is modeled by the softmax function: p$($yi $=$ k$|$xi;k$)=$ e$$ kxi K j$=1$ e$$ jxi $($a$)$ Write the conditional likelihood function for the parameters $\{$$1,$$2,...,$K$\}.($b$)$ Derive the log$-$likelihood function for multiclass classification. $($c$)$ Compute the gradient of the log$-$likelihood with respect to k$.($d$)$ Show how the cross$-$entropy loss is related to the log$-$likelihood for this classification problem.