Advanced Data Science: Modeling, Computing, & Optimization

Week	Topics	Deliverables
Week 1	Linear models (linear algebra + normal theory: projection, QR / Gram-Schmidt implications for interpretation of coefficients, SVD + Moore-Penrose)
Week 2	Dummy coding, interactions, connections to ANOVA
Week 3	Generalized linear models: Fundamentals… Exponential families + IRLS/Newton-Raphson
Week 4	Key examples of GLMs	HW 1 due
Week 5	Logistic regression (prospective/retrospective sampling, Bradley-Terry, class imbalance, etc.) + multinomial regression
Week 6	Count data (Poisson regression, mover-stayer models, connection to multinomial regression via the Poisson trick, overdispersion and the negative binomial)
Week 7	Designing and solving custom convex regularizers for data modeling (e.g., trend filtering, hierarchical sparse modeling)	HW 2 due
Week 8	Optimization methods for statistical modeling (proximal gradient, coordinate descent)
Week 9	Optimization methods for statistical modeling (continued; ADMM)
Week 10	Degrees of freedom and SURE for regularized regression	HW 3 due
Week 11	Nonparametric regression, smoothing splines, generalized additive models
Week 12	Modeling dependence with covariance estimation
Week 13	Unsupervised learning: mixture of Gaussians + EM	HW 4 due
Week 14	Unsupervised learning (continued): k-means, hierarchical, and other clustering
Week 15	Unsupervised learning (continued): PCA and UMAP	R package due

DSO 699 Week 1: Linear Models and Matrix Decompositions

Review of linear algebra foundations for statistical modeling, including projections, QR decomposition, and SVD.