ACTSC 456/856 — Weekly Schedule

A twelve-week progression through modern statistical learning techniques applied to actuarial science problems.

Topics build cumulatively: regression and classification fundamentals give way to tree-based ensembles, then to dimensionality reduction, clustering, and neural network methods. References follow James, Witten, Hastie & Tibshirani, An Introduction to Statistical Learning (ISL).

WK01

Introduction and Advance Regression I - Variable Selection

Introduction to statistical learning; Multivariate normal distribution; Review of variable selection: best subsets, stepwise (forward and backward); measures of fit (AIC, adjusted R², BIC, or cross-validation (training/test sets, k-fold, LOOCV).

ReferenceISL §2.1, 2.2
ISL §5.1, 6.1

WK02

Advanced Regression II — Penalized Methods

Penalized linear regression: ridge regression and lasso, problem formulation, and the constrained optimization view; Using cross-validation to choose the tuning parameter (λ) in ridge regression and lasso.

ReferenceISL §6.2

WK03

Advanced Regression III — High Dimensions and Non-linear Models

Principal components regression; considerations in high-dimensional settings; Regression Splines, Smoothing Splines.

ReferenceISL §6.3, 6.4
§7.1, 7.3, 7.4, 7.5

WK04

Advanced Regression IV — More Nonlinear Models

Local regression and Generalized Additive Models (GAMs).

ReferenceISL §7.6, 7.7

WK05

Classification I — Logistic Regression & LDA

Introduction to classification; logistic regression; linear discriminant analysis (LDA); confusion matrix; error rate; sensitivity and specificity; ROC curve.

ReferenceISL §4.1–4.4.2 (excl. 4.3.5)

WK06

Classification II — QDA & KNN

Quadratic discriminant analysis (QDA); K-nearest neighbours (KNN) classifier; applications of classifiers in R on actuarial and financial datasets.

ReferenceISL §2.2
ISL §4.4.3

WK07

Decision Trees I — Fundamentals

Introduction to decision trees; regression vs. classification trees; mean-square error; classification error rate; recursive binary splitting; tree pruning; cost complexity pruning.

ReferenceISL §8.1

WK08

Decision Trees II — Ensembles

Bagging, Random Forest, Boosting; applications of decision tree methodologies in R on actuarial and financial datasets.

ReferenceISL §8.2.1–8.2.3

WK09

Dimensionality Reduction

Introduction to dimensionality reduction: PCA, ICA, and t-SNE.

ReferenceISL §12.2, 12.3

WK10

Clustering

Introduction to unsupervised learning; K-means (details and examples); hierarchical clustering (dendrogram); DBSCAN.

ReferenceISL §12.1, 12.4

WK11

Advanced Clustering & Neural Networks

Introduction to neural networks (neurons and layers, activation functions, feedforward networks); Convolutional Neural Networks (CNN).

ReferenceISL §12.4, 10.1–10.4

WK12

Modern Unsupervised Learning

Classification and clustering using CNNs; introduction to autoencoders with applications to dimensionality reduction and clustering.

ReferenceISL §10.6, 10.7