MATH 7740: Statistical Learning Theory: Classification, Pattern Recognition, Machine Learning (Fall 2009)

The course aims to present the developing interface between machine learning theory and statistics. Topics include an introduction to classification and pattern recognition; the connection to nonparametric regression is emphasized throughout. Some classical statistical methodology is reviewed, like discriminant analysis and logistic regression, as well as the notion of perceptron which played a key role in the development of machine learning theory. The empirical risk minimization principle is introduced, as well as its justification by Vapnik-Chervonenkis bounds. Basic principles of constructing classifiers are treated in detail, such as support vector machines, kernelization, neural networks and tree methods. The course will conclude with an outline of boosting and aggregation as the most active research areas in learning theory today.