ASTA6002: Regression Analysis and Data Thinking

Course overview

This course covers linear models, generalized linear models, quantile regression, high-dimensional regression, variable selection, dimension reduction, and tensor regression. The focus is on understanding these models and when to use them, with particular emphasis on model interpretability and the meaning of their results.

Lasso selects important variables by setting some coefficients to zero; tensor regression uses image or tensor inputs and a coefficient tensor to predict a scalar response.

Course materials

Course materials will be continuously updated throughout the course.

Lecture 1: High-Dimensional Linear Regression and Regularization

Open the slides (PDF)

Course schedule

WeekDateTopicsSlides / module
1Nov 4
  • Ridge and Lasso
  • Best subset selection
  • Optimization and cross-validation
1
2Nov 11
  • Variable-selection theory
  • Elastic Net and adaptive Lasso
  • Structured penalties
2
3Nov 18
  • Penalized likelihood
  • IRLS and coordinate descent
  • Regularized GLMs
3
4Nov 25
  • Principal component regression
  • SIR and SAVE
  • Sufficient dimension reduction
4
5Dec 2
  • Multivariate regression
  • Reduced-rank regression
  • Sparse and low-rank models
5
6Dec 9
  • Tensor regression
  • CP and Tucker decompositions
  • Optimization and regularization
6