The <decision boundary> is the hyperplane
$$
\widehat\beta_0+x^T\widehat\beta=0.
$$
At threshold $q$ the classifier predicts spam when
$$
\widehat\beta_0+x^T\widehat\beta
>\log\frac q{1-q},
$$
so $q=1/2$ gives the original classifier. Varying $q$ translates the boundary parallel to itself: raising $q$ shrinks the region classified as spam and generally trades fewer false positives for more false negatives.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 218 / 3 / b / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-218/3/b/solution