Until now, I treated the maximal likelihood method to fit a logistic regression model always as a black box. But recently, in the paper "Categorization Based on Regularized Linear Classification methods" by T. Zhang, F.J. Oles, on on pp 10, they describe a setting that is not known to me.
Namely, they begin by considering the conditional probability $\mathbb{P}(Y=1|w,x)$. But what does "$w$" even mean ?
Earlier in the paper they only say that $w$ is a weight vector. Also, this notation "$w,x$"is not known to me. What does that mean ?
They go then on to say that they want to estimate $w$ by the maximum likelihood which minimizes
$$\hat w = \arg \inf_w (\text{"complicated function of $w,x_i,y_i$"}).$$
I assume I can make sense of this minimization only after I have understood the answers to the previous questions.