Mathematical Statistics I

The course covers advanced modern methods for high dimensional parametric statistical learning theory. Topics include: (1) Maximum likelihood and Bayesian parameter and set estimation for both iid data and Graphical Models; (2) Linear regression including ridge regression, lasso, principal components, and study of issues such as model selection and overparametrization; (3) Linear classification including Bayesian classification, discriminant analysis, Fisher discriminant analysis, flexible discriminant analysis, support vector machines, and perceptron; (4) Classical and Bayesian hypothesis testing; (5) Coherent presentation of Markov Graphical Models, Hidden Graphical models, and computational algorithms for optimization and simulation such as Markov Chain Monte, Dynamic Programming, and Bootstrap; (6) Infinite data asymptotics for inference and phase transitions for Markov Graphical Models. Prerequisite: APMA 2630 or equivalent.