STAT 591:
Concentration Inequalities
and Empirical Process Methods
for High-Dimensional Statistics
Autumn Quarter 2017
Syllabus (last updated: 9/25/17)
Course personnel:
- Professor: Jon A. Wellner
- B320 Padelford Hall
- Phone: 543-6207
- Office hours: 1:30 - 3:30 MWF; or by appointment
Time and Place:
- Time(s): 12:00 -1:30 T-Th
- Place: Padelford C-301
Prerequisites:
- Stat 581-2-3 or Stat 521-2-3 or comparable
... and an interest in high-dimensional statistics.
Textbook (required):
- Concentration Inequalities: a nonasymptotic theory of independence
Stephane Boucheron, Gabor Lugosi, Pascal Massart. Oxford University Press. (2013).
Textbooks (not required):
- Weak convergence and empirical measures.
Aad van der Vaart and Jon W. Wellner. Springer, New York. (1996)
- The Concentration of Measure Phenomenon
Michel Ledoux. American Mathematical Society. (2001)
- Statistics for High-Dimensional Data
Peter Buhlmann and Sara van de Geer. Springer, New York (2011).
- The Generic Chaining
Michel Talagrand. Springer, Heidelberg (2005).
-
Oracle inequalities in empirical risk minimization and sparse recovery problems.
Lectures from the 38th Probability Summer School held in Saint-Flour,
Lecture Notes in Mathematics 2033,
Ecole d'Ete de Probabilites de Saint-Flour. Springer.
Homeworks:
- HW1: handed out 5 October; due 19 October.
- HW2: handed out 19 October; due 2 November.
- HW3: handed out 2 November; due 16 November.
- HW4: handed out 16 November; due 30 November.
Course Description:
This course will treat inequalities for empirical processes, including concentration
inequalities of Talagrand, Bousquet, and Rio.
Methods introduced by Ledoux and Massart will also be covered,
including the Efron-Stein inequality,
Nemirovski's inequality,
and applications of these to problems in
high-dimensional statistics and machine learning, depending
on the intersts of the participants.
Further topics treated will be tailored to
the interests of the participants.
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