AMS 580: Statistical Learning

This course teaches the following fundamental topics: (1) General and Generalized Linear Models; (2) Basics of Multivariate Statistical Analysis including dimension reduction methods, and multivariate regression analysis; (3) Supervised and unsupervised statistical learning. This course will first review classical linear and generalized linear models such as Linear Regression, Logistic Regression, and Linear Discriminant Analysis. We shall then study modern Resampling Methods such as Bootstrapping, and modern variable selection methods such as the Shrinkage Method. We will study traditional multivariate analysis methods including cluster analysis, principal component analysis, and multivariate regression methods such as structural equation modeling. Finally, we shall introduce modern non-linear statistical learning methods such as the Generalized Additive Models, Decision Trees, Random Forest, Boosting, Bagging, Support Vector Machines, and Neural Networks.

Required Textbooks:

1. An Introduction to Statistical Learning with Applications in R by Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani, 2017, Springer
2. The Elements of Statistical Learning: Data Mining, Inference, and Prediction by Trevor Hastie, Robert Tibshirani and Jerome Friedman, 2nd edition, 2016, Springer
3. Applied Multivariate Statistics with R by Daniel Zelterman, 2015, Springer

Supplementary Textbook: Machine Learning: A Probabilistic Perspective by Kevin P. Murphy, 2012, MIT Press