MATH 7740 - Statistical Learning Theory

Marten Wegkamp, spring 2016.

Learning theory has become an important topic in modern statistics. I intend to give an overview of various topics in classification, starting with Stone's (1977) stunning result that there are classifiers that are universally consistent. Other topics are: classification, plug-in methods (k-nearest neighbors), reject option, empirical risk minimization, VC theory, fast rates via Mammen and Tsybakov's margin condition, convex majorizing loss functions and support vector machines, lasso type estimators and current topics in high dimensional statistics.

Students are expected to read papers and present material to the class. 

Prerequisites

Students should have knowledge of (measure theoretic) probability and mathematical statistics.

Suggested texts

BOUCHERON, S.,  BOUSQUET, O. and LUGOSI, G. (2005). Theory of Classification: a Survey of Recent Advances. ESAIM: Probability and Statistics, 9:323--375.

DEVROYE, L., GYORFI, L. and LUGOSI, G. (1996). A Probabilistic Theory of Pattern Recognition. Springer, New York.

GIRAUD, C. (2014). Introduction to High-Dimensional Statistics. Chapman & Hall.