Distribution-free inference, game and decision theory, advanced theory of estimation (including sequential estimation), robustness, advanced probability theory, stochastic processes or empirical processes. Prerequisite: permission of instructor. Offered: Sp.
This course will be on the analysis of massive high dimensional data. The topics covered will lie at the interface of statistics, mathematics and computer science. A prominent theme will be the "curse of dimensionality", i.e. exponential blow-up of statistical and computational complexity as a function of dimension, and the kind of questions in geometry, probability and algorithms, the necessity of avoiding it leads us to. We will survey some areas of research that have sprung up as a result, such as manifold learning, which is based on the hypothesis that data lie near a low dimensional manifold. Several of the topics covered will have a strong geometric flavor, and will employ ideas and/or techniques from differential and computational geometry, functional analysis and optimization.
Student learning goals
General method of instruction
Familiarity with probability and some experience with high dimensional geometry is desirable.
Class assignments and grading