36-709 Advanced Statistical Theory I

12 units, Carnegie Mellon University

This is a core Ph.D. course in theoretical statistics. The class will cover a selection of modern topics in mathematical statistics, focussing on high-dimensional parametric models and non-parametric models. The main goal of the course is to provide the students with adequate theoretical background and mathematical tools to read and understand the current statistical literature on high-dimensional models. Topics will include: concentration inequalities, covariance estimation, principal component analysis, penalized linear regression, maximal inequalities for empirical processes, Rademacher and Gaussian complexities, non-parametric regression and minimax theory. This will be the first part of a two semester sequence.

Prerequisites: 36-705

Offered: Spring 2027, Spring 2026

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