STAT 200B: Statistical Theory

Ying Nian Wu, MWF 1:00 PM-1:50 PM, FRANZ 2258A

Office hours: MW 11-12pm, 8971 Math Sci Bldg

This is a graduate course on the theory of statitical inference and learning.

Topics:
(1) Modes of statistical inference: point estimate, hypothesis testing, confidence interval, likelihood, sufficiency, Bayesian inference, decision theory, Stein estimator. (running examples: inference of binomial probability and normal means)
(2) Linear regression: best linear unbiased estimator, model complexity, training error and testing error, bias and variance, L2 and L1 regularization.
(3) Maximum likelihood: asymptotic optimality among estimating equations, Fisher information, Cramer-Rao bound, EM, likelihood ratio test, Akaike information criterion. (running examples: logistic regression, exponential family model, mixture model, latent variables and missing data, goodness of fit test, test of independence)
(4) Machine learning: PAC learning, VC dimension, perceptron, SVM, adaboost, unsupervised learning. (presented from a statistician's perspective)

Textbooks: None.

Coursework:
(1) Attenance (20%) enforced by quizzes.
(2) Weekly homework (40%). Due every Friday in class. You are allowed to discuss with your fellow students about homework, but you must work on the problems and write the solutions by yourself. It is not allowed to share paragraphs or code.
(3) Midterm (20%, Friday Feb 10, 2012, in class. A review lecture will be given by TA on Feb 8).
(4) Final exam (20%, take home). You are not allowed to discuss with others.