Here is the reference: http://nlp.chonbuk.ac.kr/BML/slides_freda/lec7.pdf
We know that logistic regression is implemented by Iteratively Reweighted Least Squares (IRLS), we have the final iteration formula of parameter $\theta:$
$$\theta^{k+1} = \theta^{k} - (H^k)^{-1}g^k$$
$$\Rightarrow\theta^{k+1} = (X^TS^kX)X^TS^kz^k,$$
$$z^k \triangleq X\theta^k+(S^k)^{-1}(y - \mu^k).$$
Here I ignore the statement of notations. From formula: $(X^TS^kX)X^TS^kz^k$ we know that it is the solution of General Least Square with error covariance inverse $(S^k)^{-1}.$ Since $S^k$ is diagonal. Then it degenerates as a Reweighted Least Squares.
I think the conclusion is purely from the result formula, is there any intuitive explanation before we know the result formula?
