Can we use Normal Equation for Logistic Regression

Question

Just like we use the Normal Equation to find out the optimum theta value in Linear Regression, can/can't we use a similar formula for Logistic Regression ?

Answer 1

Well not likely,  only one discriminative method in classification theory, linear regression... (linear discriminant analysis/fischer discriminant are generative, and even they have a closed form solution due to the extreme simplicity of the distributions fitted).
So, what made Normal Equation so successful in linear regression? Because once you've computed your derivatives, you'll find that the outcome is a set of linear equations, m equations with m variables, which we know can be solved directly using matrix inversions (and other techniques). When logistic regression costs are differentiated, the resultant issue is no longer linear... it is convex (thus global optimum), but not linear, and as a result, present mathematics does not offer us with tools powerful enough to identify the optimum in closed form solution.