Let's derive this loss function, applied to a single observation x. We'd like to learn weights that maximize the probability of the correct label p(y|x). Since there are only two discrete outcomes (1 or 0), this is a Bernoulli distribution, and we can express the probability p(y|x) that our classifier produces for one observation as the following (keeping in mind that if y=1, Eq. 5.9 simplifies toŷ; if y=0, Eq. 5.9 simplifies to 1 −ŷ):