Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Paper 1 / 15 / b / Solution

Include an intercept $w_0$ and let $\mathbf{z}$ be the chosen numerical feature vector. Logistic regression usesThe logistic function maps every real score into $(0,1)$, allowing a Bernoulli distribution model for the label. Equivalently, the log odds are linear in the features:This gives a smooth differentiable probability model with a linear decision boundary at any fixed probability threshold. The sigmoid output is a fitted conditional probability, not a categorical prediction until a threshold is chosen.