Supervised Learning

Study guides: Exam MAS-I, Exam MAS-II

Supervised learning fits a model to predict a labelled response Y from predictors X. Every observation in the training data carries the answer, so the fit can be scored against it — the defining contrast with Unsupervised Learning.

Y = f(X) + \varepsilon

\hat{Y} = \hat{f}(X)

• Regression predicts a numeric Y (pure premium, severity) and is scored by squared error; classification predicts a class (fraud / not) and is scored by error rate, AUROC or the Confusion Matrix
• Syllabus methods (CAS 2026 outlines): MAS-I — Linear Regression, Logistic Regression, Quadratic Discriminant Analysis, Naive Bayes and the Generalized Linear Model; subset selection (Variable Selection), ridge and lasso (Regularization), Principal Components Regression and Partial Least Squares; Polynomial Regression, Step Functions, Regression Splines, Smoothing Splines, Local Regression and Generalized Additive Models. MAS-II — K-Nearest Neighbors, Decision Trees, Tree Ensembles (Bagging, Random Forest, Boosting) and Neural Networks
• The goal is test error, not training error — flexible methods drive training error to zero and generalize badly (Bias-Variance Tradeoff)
• Test error is estimated by a held-out set or by Cross-Validation
• Parametric methods assume a form for f and estimate a few coefficients; non-parametric ones (KNN, for example) let the data set the shape, needing far more of it

Which Task Is This? Classify each: (a) predicting a policy's expected claim count next year; (b) flagging claims likely to be fraudulent, given past investigated claims; (c) grouping 68 territories into five rating regions from their loss characteristics.

Answer (a) Supervised regression — the response is a count and history supplies it. (b) Supervised classification — the investigated claims carry a fraud/no-fraud label. (c) Unsupervised — there is no "correct region" label to fit against; this is Clustering.