an .5.
And as you can see from the plot of the logistic sigmoid, the probability of the class +1 is greater than .5
exactly if the decision function $w^T x$ is greater than 0.
So predicting the class with maximum probability is the same as predicting which side of the hyperplane
given by w we are on.

Ok so this is logistic regression. We minimize this loss and get a w which defines a hyper plane.
But if you think back to last time, this is only part of what we want. This formulation
tries to fit the traini