For logistic regression, there is no longer a closed$-$form solution, due to the nonlinearity

of the logistic sigmoid function. the error function can be minimized by an efficient

iterative technique based on the Newton$-$Raphson iterative optimization scheme

a$.$ Provide the expressions of the gradient, Hessian, and update equations for the

Newton$-$Raphson optimization technique used to obtain the parameters in the

logistic regression model. Provide an algorithm describing the methodology.

b$.$ Show that the Newton$-$Raphson update scheme is related to the weighted least

squares problem described in question $3($c$)$ and explain why it is called the

iterative reweighted least squares method.

c$.$ Show that the error function of the logistic regression is a concave function of w

and hence has a unique minimum with the help of the Hessian matrix.