Course description
The course is an introduction to the non-asymptotic statistical analysis of high-dimensional and nonparametric models. The goal is to prepare students for the fundamental notions of statistics required for research in statistics, statistical learning and related topics. Includes: linear and nonparametric regression, covariance estimation, principal component analysis, sparsity, minimax lower bounds, prediction and margin analysis for classification. We will develop a rigorous probabilistic toolkit, including tail bounds and a basic theory of empirical processes.Target audience:
Graduate students with a solid grasp of probability. This course will satisfy the “Statistics” requirement for the Interdisciplinary Program in Statistics (IDPS). The course will not cover the classical topics (such as confidence intervals, hypothesis testing, decision theory, sufficiency, exponential families, etc). Students interested in these topics are encouraged to take 18.6501 and/or 18.655.Course numbers:
The same class is offered under the following three course numbers: IDS.160, 9.521 and 18.S998. Students may register for either of these.Prerequisites:
- Linear algebra at the level of 18.06 or equivalent.
- A graduate course in probability at the level of 18.675 or 6.436 is ideal, but undergraduate courses at the level of 18.600 or 6.041 might suffice if coupled with general mathematical maturity and exposure to analysis.
- Suggested: a course on classical statistics (at the level of 18.6501).
Resources (not required):
- Martin Wainwright, High-Dimensional Statistics: A Non-Asymptotic Viewpoint.
- Philippe Rigollet and Jan-Christian Huetter, High Dimensional Statistics. Lecture Notes
- Roman Vershynin, High-Dimensional Probability: An Introduction with Applications in Data Science
