Support Vector Machines for Insurance Classification

Maximal Margin Classifier

The maximal margin classifier finds the hyperplane that separates two classes with the largest margin (the distance from the hyperplane to the nearest data points). The data points closest to the hyperplane are called support vectors. The decision boundary depends only on these support vectors, not on other observations far from the boundary.

For data that is not linearly separable, the maximal margin classifier does not exist, motivating the soft margin approach.

Support Vector Classifier (Soft Margin)

The support vector classifier allows some observations to be on the wrong side of the margin or even the hyperplane, controlled by slack variables and a cost parameter C. The optimization minimizes (1/2)||w||^2 + C * sum(xi_i), where xi_i are slack variables. Large C penalizes misclassifications heavily (narrow margin, low bias, high variance); small C allows more misclassifications (wide margin, higher bias, lower variance). C is chosen by cross-validation.

Kernel SVMs

For non-linear boundaries, SVMs use the kernel trick: replace the dot product x_i' * x_j with a kernel function K(x_i, x_j) that implicitly maps data to a higher-dimensional space. Common kernels: polynomial K(x, x') = (1 + x'x')^d and radial basis function (RBF) K(x, x') = exp(-gamma * ||x - x'||^2). The RBF kernel can model highly non-linear boundaries. For Exam SRM, understand that SVMs are effective for binary classification, especially with moderate-sized datasets. They are less interpretable than logistic regression or decision trees but can capture complex boundaries. Kernel choice and the C parameter are the main tuning decisions.