MATH 7740

Statistical Learning Theory: Classification, Pattern Recognition, Machine Learning

Course Description

Course information provided by the Courses of Study 2020-2021.

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 perception 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. In addition, convex majoring loss functions and margin conditions that ensure fast rates and computable algorithms are discussed. Today's active high-dimensional statistical research topics such as oracle inequalities in the context of model selection and aggregation, lasso-type estimators, low rank regression and other types of estimation problems of sparse objects in high-dimensional spaces are presented.

When Offered Fall.

Prerequisites/Corequisites Prerequisite: basic mathematical statistics (MATH 6730 or equivalent) and measure theoretic probability (MATH 6710).

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